IRV proponents figure out how to make IRV precinct-summable

[Kathy Dopp]

Wow,

I had to laugh out loud after finally figuring out these instructions
that Chris Telesca of NC sent me in this PDF doc:

"Instant Runoff Voting, Single‐Seat Contests, ES&S Optical Scan
Tabulation Procedures"

http://electionmathematics.org/em-IRV/NC/IRVcountingProced.pdf

Aren't IRV proponents (of the most fundamentally unfair voting method
that has ever been used) CLEVER!

IRV proponents have figured out how to count a NC-style IRV election
(where all but the top two candidates are dropped in the first round)
in the polling locations on Election Night in a way that makes
IRV-NC-style precinct-summable!

Wow. I'm really impressed for once by the skills of the IRV proponents
in figuring out a way to make round #2 of IRV precinct-summable -
which works in the NC version of IRV because all but two candidates
are eliminated in round #1.

However, there are some issues with the IRV proponents' method for
making IRV precinct-summable in this NC-style IRV contest that also
restricts voters to ranking at most three candidates and therefore has
at most two counting rounds altogether for a one-winner contest due to
eliminating all but the two candidates who receive the most first
choice votes (a method that could often eliminate the most popular
majority candidate as happened recently in Burlington, VT
http://rangevoting.org/Burlington.html)

Here is what I'd like to ask about conducting these IRV
precinct-summable counts for round #2:

1. Are election officials and poll workers genius-level enough and
focused enough to comprehend the instructions and to follow them
without making errors?

Link to the virtually incomprehensible instructions is here:
http://electionmathematics.org/em-IRV/NC/IRVcountingProced.pdf

2. Just how sturdy are the paper ballots?

This "precinct-summable" IRV counting method requires (to accomplish
just one counting round - round #2 only) feeding each ballot one at a
time by hand through the precinct opti-scanners up to four times with
the optical scanner needing a differently programmed PCMCIA card in it
for each count for EACH IRV ELECTION CONTEST and poll workers must pay
close attention to whether or not each ballot is "rejected" or
"accepted" and put each ballot in a correct pile depending on which
stack it comes from and whether it is rejected or accepted by the
M100.

(Note this is to only count ONE IRV counting round since the first
round is assumed to be counted and all but the top two 1st choice
vote-getters are "eliminated" in the first step of M100 reprogramming
that the poll workers have to do between each count - as far as I
could tell. In fact, the PCMCIA cards may also have to programmed or
burned in three separate ways at the poll locs as well - the
instructions left out crucial details of exactly how to "burn" the
PCMCIA cards.

3. What an amazingly long time is it going to take to count all the
ballots in each precinct for each of the IRV contests for just this
one IRV round?

I.e. the ballots would have to be accurately sorted into four piles
during the first feed (one ballot at a time) into the precinct
scanners,

and then sorted into five piles (sorted to four piles coming out of
the optiscanner plus one pile not run through it) during the second
feed (one ballot at a time) into the precinct scanners,

and then sorted into six total piles (sorted to three piles coming out
of the optical scanner plus two piles not run through it this time)
during the third feed (one ballot at a time) into the precinct
scanners,

and then sorted into seven total piles (sorted to two piles coming out
of the optiscanner plus five piles not run through it this time (one
ballot at a time) into the precinct scanners.

It will be nothing short of a praise the Lord miracle if this process
is performed accurately in all polling locations.

The press might as well go home and come back in the a.m. and the poll
workers might as well plan to stay up all night to try to get this
process right for EACH IRV contest. I hope that they plan on an
all-new shift of poll workers coming in to every polling place to
accomplish this task of counting all the IRV contests by running the
IRV ballots through the M100s one at a time four times for EACH
contest and reprogramming M100s numerous times to do it.

4. Are the election officials going to create the three PCMCIA cards
accurately for EACH precinct or poll loc for each IRV contest, label
them accurately and make sure that the right card is inserted at the
exact right time in the process?

Purchases must be made of at least 3 extra PCMCIA cards for EACH
polling place and buying 3 backup PCMCIA cards for each polling place
would be helpful as well in case any of them fail when poll workers
are trying to configure and burn them all.

I suppose another option in case the poll workers can't figure it out,
would be for the central county office to burn all the extra PCMCIA
cards after it is known which candidates did not receive the top-two
1st choice votes and poll-workers can simply wait until someone from
the county office delivers all the correctly programmed and correctly
labeled PCMCIA cards.

5. How are the poll workers going to correctly reprogram the M100
optical scanners between each of the four separate counts they'll have
to do for EACH IRV contest for EACH precinct or polling location (from
what I can tell)?

6. Wow. I would LOVE to see what happens if the late-counted absentee,
early, or provisional ballots changes who the top-two 1st choice vote
winners are, and the entire polling location counts have to be thrown
out and all the ballots have to be recounted! Lovely thought for all
those poll workers who are going to stay up all night counting but
whose counts may be entirely scrapped later on whenever the number of
first choice votes is very close for the candidate with the second
most and third most first choice votes!

This should be an amusing MESS of gargantuan proportions if any NC
township or county is INSANE enough to attempt counting IRV ballots by
using this method!!

AMAZING. No election official with any semblance of a right mind
would support doing these procedures in all poll locs on election
night IMO.

Combined with the recent evidence from the Burlington Nov 2008
election showing how IRV (including the NC variety) fails to elect
majority winners or solve the spoiler problem and can easily be
nonmonotonic, I hope that this proposed process will kill IRV
proposals, at least in NC.

Eventually sanity may prevail.

Notice how closely ES&S worked with IRV proponents to create these
instructions. If only the voting vendors would work that closely with
election integrity advocates - but then the financial benefits to
voting vendors if IRV is adopted are enormous and the costs to
election integrity and fairness of adopting IRV are enormous too.

It is interesting to see from this document how poorly designed the
ES&S programming of its machines is for doing things like checking the
accuracy of its machine counts after elections though. ES&S obviously
was given the same design specifications as Diebold, Hart Intercivic,
Sequoia, were given.

Cheers,
--
Kathy Dopp

The material expressed herein is the informed product of the author's
fact-finding and investigative efforts. Dopp is a Mathematician,
Expert in election audit mathematics and procedures; in exit poll
discrepancy analysis; and can be reached at

P.O. Box 680192
Park City, UT 84068
phone [phone]

http://utahcountvotes.org
http://electionmathematics.org
http://kathydopp.com/serendipity/

Post-Election Vote Count Audit
A Short Legislative & Administrative Proposal
http://electionmathematics.org//ucvAnalysis/US/paper-audits/Vote-Count-Audit-Bill-2009.pdf

History of Confidence Election Auditing Development & Overview of
Election Auditing Fundamentals
http://electionarchive.org/ucvAnalysis/US/paper-audits/History-of-Election-Auditing-Development.pdf

Voters Have Reason to Worry
http://utahcountvotes.org/UT/UtahCountVotes-ThadHall-Response.pdf
----
Election-Methods mailing list - see http://electorama

[Kathy Dopp]

Wow,

I had to laugh out loud after finally figuring out these instructions
that Chris Telesca of NC sent me in this PDF doc:

"Instant Runoff Voting, Single‐Seat Contests, ES&S Optical Scan
Tabulation Procedures"

http://electionmathematics.org/em-IRV/NC/IRVcountingProced.pdf

Aren't IRV proponents (of one of the most fundamentally unfair voting
methods in use today) CLEVER!

IRV proponents have figured out how to count a NC-style IRV election
(where all but the top two candidates are dropped in the first round)
in the polling locations on Election Night in a way that makes
IRV-NC-style precinct-summable!

Wow. I'm really impressed for once by the skills of the IRV proponents
in figuring out a way to make one round (round #2) of IRV
precinct-summable - which works in the NC version of IRV because all
but two candidates are eliminated in round #1.

However, there are some issues with the IRV proponents' method for
making IRV precinct-summable in this NC-style IRV contest where NC
also restricts voters to ranking at most three candidates and
therefore has at most two counting rounds altogether for a one-winner
contest due to eliminating all but the two candidates who receive the
most first choice votes (a method that could often eliminate the most
popular majority candidate as happened recently in Burlington, VT
http://rangevoting.org/Burlington.html)

Here is what I'd like to ask about conducting these IRV
precinct-summable counts for round #2:

1. Are election officials and poll workers genius-level enough and
focused enough to comprehend the instructions and to follow them
without making errors?

Link to the virtually incomprehensible instructions is here:
http://electionmathematics.org/em-IRV/NC/IRVcountingProced.pdf

2. Just how sturdy are the paper ballots?

This "precinct-summable" IRV counting method requires (to accomplish
just one counting round - round #2 only) feeding each ballot one at a
time by hand through the precinct opti-scanners up to four times with
the optical scanner needing a differently programmed PCMCIA card in it
for each count for EACH IRV ELECTION CONTEST and poll workers must pay
close attention to whether or not each ballot is "rejected" or
"accepted" and put each ballot in a correct pile depending on which
stack it comes from and whether it is rejected or accepted by the
M100.

(Note this is to only count ONE IRV counting round since the first
round is assumed to be counted and all but the top two 1st choice
vote-getters are "eliminated" in the first step of M100 reprogramming
that the poll workers have to do between each count - as far as I
could tell. In fact, the PCMCIA cards may also have to programmed or
burned in three separate ways at the poll locs as well - the
instructions left out crucial details of exactly how to "burn" the
PCMCIA cards.

3. What an amazingly long time is it going to take to count all the
ballots in each precinct for each of the IRV contests for just this
one IRV round?

I.e. the ballots would have to be accurately sorted into four piles
during the first feed (one ballot at a time) into the precinct
scanners,

and then sorted into five piles (sorted to four piles coming out of
the optiscanner plus one pile not run through it) during the second
feed (one ballot at a time) into the precinct scanners,

and then sorted into six total piles (sorted to three piles coming out
of the optical scanner plus two piles not run through it this time)
during the third feed (one ballot at a time) into the precinct
scanners,

and then sorted into seven total piles (sorted to two piles coming out
of the optiscanner plus five piles not run through it this time (one
ballot at a time) into the precinct scanners.

It will be nothing short of a praise the Lord miracle if this process
is performed accurately in all polling locations.

The press might as well go home and come back in the a.m. and the poll
workers might as well plan to stay up all night to try to get this
process right for EACH IRV contest. I hope that they plan on an
all-new shift of poll workers coming in to every polling place to
accomplish this task of counting all the IRV contests by running the
IRV ballots through the M100s one at a time four times for EACH
contest and reprogramming M100s numerous times to do it.

4. Are the election officials going to create the three PCMCIA cards
accurately for EACH precinct or poll loc for each IRV contest, label
them accurately and make sure that the right card is inserted at the
exact right time in the process?

Purchases must be made of at least 3 extra PCMCIA cards for EACH
polling place and buying 3 backup PCMCIA cards for each polling place
would be helpful as well in case any of them fail when poll workers
are trying to configure and burn them all.

I suppose another option in case the poll workers can't figure it out,
would be for the central county office to burn all the extra PCMCIA
cards after it is known which candidates did not receive the top-two
1st choice votes and poll-workers can simply wait until someone from
the county office delivers all the correctly programmed and correctly
labeled PCMCIA cards.

5. How are the poll workers going to correctly reprogram the M100
optical scanners between each of the four separate counts they'll have
to do for EACH IRV contest for EACH precinct or polling location (from
what I can tell)?

6. Wow. I would LOVE to see what happens if the late-counted absentee,
early, or provisional ballots changes who the top-two 1st choice vote
winners are, and the entire polling location counts have to be thrown
out and all the ballots have to be recounted! Lovely thought for all
those poll workers who are going to stay up all night counting but
whose counts may be entirely scrapped later on whenever the number of
first choice votes is very close for the candidate with the second
most and third most first choice votes!

This should be an amusing MESS of gargantuan proportions if any NC
township or county is INSANE enough to attempt counting IRV ballots by
using this method!!

AMAZING. No election official with any semblance of a right mind
would support doing these procedures in all poll locs on election
night IMO.

Combined with the recent evidence from the Burlington Nov 2008
election showing how IRV (including the NC variety) fails to elect
majority winners or solve the spoiler problem and can easily be
nonmonotonic, I hope that this proposed process will kill IRV
proposals, at least in NC.

Eventually sanity may prevail.

Notice how closely ES&S worked with IRV proponents to create these
instructions. If only the voting vendors would work that closely with
election integrity advocates - but then the financial benefits to
voting vendors if IRV is adopted are enormous and the costs to
election integrity and fairness of adopting IRV are enormous too.

It is interesting to see from this document how poorly designed the
ES&S programming of its machines is for doing things like checking the
accuracy of its machine counts after elections though. ES&S obviously
was given the same design specifications as Diebold, Hart Intercivic,
Sequoia, were given.

Cheers,
--
Kathy Dopp

The material expressed herein is the informed product of the author's
fact-finding and investigative efforts. Dopp is a Mathematician,
Expert in election audit mathematics and procedures; in exit poll
discrepancy analysis; and can be reached at

P.O. Box 680192
Park City, UT 84068
phone [phone]

http://utahcountvotes.org
http://electionmathematics.org
http://kathydopp.com/serendipity/

Post-Election Vote Count Audit
A Short Legislative & Administrative Proposal
http://electionmathematics.org//ucvAnalysis/US/paper-audits/Vote-Count-Audit-Bill-2009.pdf

History of Confidence Election Auditing Development & Overview of
Election Auditing Fundamentals
http://electionarchive.org/ucvAnalysis/US/paper-audits/History-of-Election-Auditing-Development.pdf

Voters Have Reason to Worry
http://utahcountvotes.org/UT/UtahCountVotes-ThadHall-Response.pdf
----
Election-Methods mailing list - see http

[Kathy Dopp]

Apologies for the double post and my logic error of stating that the
IRV proponents with the help of ES&S found a way to make IRV
precinct-summable when of course they only found a way to count one of
the easiest possible IRV rounds (one with only two candidates
continuing in the contest) using today's optical scanners using an
incredibly ugly method that anyone would have to be insane to try
using.

Here is my revised post on this topic:

http://kathydopp.com/serendipity/index.php?/archives/41-IRV-proponents-figure-out-how-to-count-IRV-with-todays-precinct-opti-scanners-for-restricted-case.html

It is entertaining IMO.

And at least I detected my own logic error before anyone had to point
it out to me, as I'm sure someone on this list would have.

Cheers,

Kathy
----
Election-Methods mailing list - see http://electorama.com/em for list info

[Kristofer Munsterhjelm]

Post by Kathy Dopp
Wow,
I had to laugh out loud after finally figuring out these instructions
"Instant Runoff Voting, Single‐Seat Contests, ES&S Optical Scan
Tabulation Procedures"
http://electionmathematics.org/em-IRV/NC/IRVcountingProced.pdf
Aren't IRV proponents (of the most fundamentally unfair voting method
that has ever been used) CLEVER!
IRV proponents have figured out how to count a NC-style IRV election
(where all but the top two candidates are dropped in the first round)
in the polling locations on Election Night in a way that makes
IRV-NC-style precinct-summable!

Sure - if you have an elimination method where you batch eliminate all
candidates but k, where k is some constant, then do a count among those,
that method will be summable. Since k is a constant, k! will also be.
The constant would be extremely large for large numbers of k, though.

I wouldn't call this method IRV, either, but "contingent vote". About
the only thing it has going over Plurality is that it never elects a
Condorcet loser.

The summable version for k = 2 would work like this: you have an array
of n, which is the Plurality count for the first election. Then you have
an n*n matrix, call it c, where c[a, b] designates how many times A is
ranked before B. The idea would be to first determine the two Plurality
winners, then (call them x and y) check if c[x, y] > c[y, x]. If so, x
wins; if c[x, y] < c[y, x], then y wins, otherwise there's a tie.

But hold on. Isn't c the Condorcet matrix?

Post by Kathy Dopp
Wow. I'm really impressed for once by the skills of the IRV proponents
in figuring out a way to make round #2 of IRV precinct-summable -
which works in the NC version of IRV because all but two candidates
are eliminated in round #1.
However, there are some issues with the IRV proponents' method for
making IRV precinct-summable in this NC-style IRV contest that also
restricts voters to ranking at most three candidates and therefore has
at most two counting rounds altogether for a one-winner contest due to
eliminating all but the two candidates who receive the most first
choice votes (a method that could often eliminate the most popular
majority candidate as happened recently in Burlington, VT
http://rangevoting.org/Burlington.html)

That almost turns it into the Supplementary Vote (where people can only
rank two candidates).

Post by Kathy Dopp
4. Are the election officials going to create the three PCMCIA cards
accurately for EACH precinct or poll loc for each IRV contest, label
them accurately and make sure that the right card is inserted at the
exact right time in the process?

This sounds like simply bad programming. Having to use different PCMCIA
cards is a limitation of the voting machine, not the system; and if they
really want to use this method, they could presumably ask for a machine
that counts c (and the Plurality counts) in one go. If c really is the
Condorcet matrix, this may make it easier to move to Condorcet methods
in the future, too.

Post by Kathy Dopp
6. Wow. I would LOVE to see what happens if the late-counted absentee,
early, or provisional ballots changes who the top-two 1st choice vote
winners are, and the entire polling location counts have to be thrown
out and all the ballots have to be recounted! Lovely thought for all
those poll workers who are going to stay up all night counting but
whose counts may be entirely scrapped later on whenever the number of
first choice votes is very close for the candidate with the second
most and third most first choice votes!

I don't see how that would be messy. Say the plurality count is 100 A,
99 B, and c[A, B] is 125 and c[B, A] is 124. Then adding a few more B
first, A second ballots will change the plurality count (to say, 101 A,
105 B), and c (to say c[A, B] 131, c[B, A] 125). The actual winner
calculation would proceed differently, but since the method is district
summable, it's also individually summable ("districts" of one per voter).
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[Kathy Dopp]

On Tue, Mar 17, 2009 at 3:54 AM, Kristofer Munsterhjelm

Post by Kristofer Munsterhjelm
Sure - if you have an elimination method where you batch eliminate all
candidates but k, where k is some constant, then do a count among those,
that method will be summable. Since k is a constant, k! will also be. The
constant would be extremely large for large numbers of k, though.

Well there were two candidates left, and three possible candidate
rankings and 13 separate piles of ballots altogether with at most 7
piles at a time using their method.

Post by Kristofer Munsterhjelm
I wouldn't call this method IRV, either, but "contingent vote". About the
only thing it has going over Plurality is that it never elects a Condorcet
loser.
The summable version for k = 2 would work like this: you have an array of n,
which is the Plurality count for the first election. Then you have an n*n
matrix, call it c, where c[a, b] designates how many times A is ranked
before B. The idea would be to first determine the two Plurality winners,
then (call them x and y) check if c[x, y] > c[y, x]. If so, x wins; if c[x,
y] < c[y, x], then y wins, otherwise there's a tie.

Your method if it is correct for this version of IRV is not the same
as theirs, maybe better but they were solving the problem of counting
with today's voting machines. You are assuming whatever programming
capacity you need in the machines.

Post by Kristofer Munsterhjelm
This sounds like simply bad programming. Having to use different PCMCIA
cards is a limitation of the voting machine,

Yes, today's voting systems are unimaginably flawed and most states
require federal certification to the voluntary voting system
guidelines which is a joke and a process that takes years to go
through to get a new system that is likely to be antiquated by the
time it is certified, etc. (our entire system for implementing voting
machines is a mess today)

Post by Kristofer Munsterhjelm
I don't see how that would be messy. Say the plurality count is 100 A, 99 B,
and c[A, B] is 125 and c[B, A] is 124.

HELLO. I'm living in REALITY AS it exists today, not in some fantasy
land where you use vaporware to count the votes.

YES it IS a MESS to count IRV using this method given we're living
TODAY NOW, without your vaporware.
--
Kathy Dopp

The material expressed herein is the informed product of the author's
fact-finding and investigative efforts. Dopp is a Mathematician,
Expert in election audit mathematics and procedures; in exit poll
discrepancy analysis; and can be reached at

P.O. Box 680192
Park City, UT 84068
phone [phone]

http://utahcountvotes.org
http://electionmathematics.org
http://kathydopp.com/serendipity/

Post-Election Vote Count Audit
A Short Legislative & Administrative Proposal
http://electionmathematics.org//ucvAnalysis/US/paper-audits/Vote-Count-Audit-Bill-2009.pdf

History of Confidence Election Auditing Development & Overview of
Election Auditing Fundamentals
http://electionarchive.org/ucvAnalysis/US/paper-audits/History-of-Election-Auditing-Development.pdf

Voters Have Reason to Worry
http://utahcountvotes.org/UT/UtahCountVotes-ThadHall-Response.pdf
----
Election-Methods mailing list - see http://electorama.com/em for list info

[Kathy Dopp]

There has been a lot of guessing - let's see if I can do better, though
Precinct-summable IRV is not reachable.  The first counts of top ranks have
to be centrally summed to identify certain losers.  Then for each ballot of
such a loser the next-ranked not-yet-lost candidate must be reported.
     Have precinct do it, since they have the ballots.
     Have had ballot images forwarded so central can do the count.

I agree with you David. And BTW, I also agree with most of what
Kristofer said and in retrospect did not mean that his software idea
was "vaporware" so much as that it would take at least 4 years to be
federally certified at the cost of hundreds of thousands of dollars
just for the certification so that it is "vaporware" only from that
sense of not being available for most states to use for a long time.

The federal-state voting system certification process is a mess and
the entire voting machine industry is a mess because they use
proprietary standards and so voting system component are not
interoperable, and the flawed design of voting machines makes it
extremely difficult to check to see if the systems are producing
accurate vote counts or not.

BTW, I edited to improve the accuracy and informativeness of my blog
today, so please give it a second look:

http://kathydopp.com/serendipity/index.php?/archives/41-NC-BOE-figures-out-how-to-count-IRV-with-todays-precinct-opti-scanners.html

Thanks.

Kathy
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[Kristofer Munsterhjelm]

Post by Kathy Dopp

There has been a lot of guessing - let's see if I can do better, though
Precinct-summable IRV is not reachable. The first counts of top ranks have
to be centrally summed to identify certain losers. Then for each ballot of
such a loser the next-ranked not-yet-lost candidate must be reported.
Have precinct do it, since they have the ballots.
Have had ballot images forwarded so central can do the count.

I agree with you David. And BTW, I also agree with most of what
Kristofer said and in retrospect did not mean that his software idea
was "vaporware" so much as that it would take at least 4 years to be
federally certified at the cost of hundreds of thousands of dollars
just for the certification so that it is "vaporware" only from that
sense of not being available for most states to use for a long time.

I would say that the only way to make it summable is to do it my way, or
at least emulate my way. From what you say, it seems that they make it
"summable" by eliminating all but two candidates and then seeing which
one wins; that is, they run a "fake first round" for all possible
combinations of winner candidates. Then a Plurality count determines who
those two winner candidates are. My claim is then that of some winner
set {X, Y} of two candidates (possible two round result), X wins iff
c[X, Y] > c[Y, X]. That means that their method is a hackish variant of
mine, where the hack is required because they're stuck with currently
certified voting machines.

By the way, I don't see Dave's post to which you replied. Is it just me?

Post by Kathy Dopp
The federal-state voting system certification process is a mess and
the entire voting machine industry is a mess because they use
proprietary standards and so voting system component are not
interoperable, and the flawed design of voting machines makes it
extremely difficult to check to see if the systems are producing
accurate vote counts or not.

To the extent of my knowledge, I agree. I think that having the machines
be engineered around a summable method would help a lot - then the
machines could be, to quote someone whose name escapes me at the moment,
"expensive pencils". A Condorcet counting machine simply has to do the
very simple job of iterating through the ranks; a Range counting machine
just has to turn optical scan configurations into numbers ("he filled
in three circles of ten for candidate X" to "X: 3/10"). You're left with
a small amount of information - the sum of the array or matrix - that
can be made public.

That may sound more vaporware-ish, but what I'm trying to say is that:
if we could only have one change, let that be that rank order machines
use a format that is summable and can be used by a variety of methods.
Condorcet matrices fit (most Condorcet methods only need the matrix).
Weighted positional methods (Borda, etc) can all use another kind of
matrix ({x,y} contains the number equal to how many times candidate x
was voted in yth place). And so on... what you have to decide is what
format to use.
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[Kathy Dopp]

On Tue, Mar 17, 2009 at 5:09 PM, Kristofer Munsterhjelm

I would say that the only way to make it summable is to do it my way, or at
least emulate my way. From what you say, it seems that they make it
"summable" by eliminating all but two candidates and then seeing which one
wins; that is, they run a "fake first round" for all possible combinations
of winner candidates. Then a Plurality count determines who those two winner
candidates are.

That is not quite what they do. They count the first round at the
central office by counting only the 1st choice votes, and eliminate
all but the top two 1st choice vote winners. Then, they count the 2nd
and last round in the polling places. I can see poll workers waiting
around in the polls until perhaps as late as 11 p.m. waiting to get
the first round results so that they can begin counting the second
round.

They can of course eliminate the majority-favorite candidate in the
first round this way, since this uses the typical IRV method for
counting the 2nd, 3rd choices of only some voters depending on if
their first or second choice is one of the top two or not.

My claim is then that of some winner set {X, Y} of two
candidates (possible two round result), X wins iff c[X, Y] > c[Y, X]. That
means that their method is a hackish variant of mine, where the hack is
required because they're stuck with currently certified voting machines.

Let's hope that your method is better than theirs since theirs is
nonmonotonic and does not find majority-favored winners.

By the way, I don't see Dave's post to which you replied. Is it just me?

I included it in my email. He may not have sent it to the list.

To the extent of my knowledge, I agree. I think that having the machines be
engineered around a summable method would help a lot - then the machines
could be, to quote someone whose name escapes me at the moment, "expensive
pencils". A Condorcet counting machine simply has to do the very simple job
of iterating through the ranks; a Range counting machine  just has to turn
optical scan configurations into numbers ("he filled in three circles of ten
for candidate X" to "X: 3/10"). You're left with a small amount of
information - the sum of the array or matrix - that can be made public.

Yes. I agree that any of those methods are simpler to count then IRV
and produces far more fundamentally fair, desirable results.

That may sound more vaporware-ish, but what I'm trying to say is that: if we
could only have one change, let that be that rank order machines use a
format that is summable and can be used by a variety of methods. Condorcet
matrices fit (most Condorcet methods only need the matrix). Weighted
positional methods (Borda, etc) can all use another kind of matrix ({x,y}
contains the number equal to how many times candidate x was voted in yth
place). And so on... what you have to decide is what format to use.

I would think that the particular programming method would have to be
unique for the method and yet we need to use a summable method.

Lucky for North Carolina that their State election statutes prohibit
voting methods that cannot be counted in the precincts so that they
are seemingly saved from the vagaries of IRV.

Cheers,

Kathy
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[Kristofer Munsterhjelm]

Post by Kristofer Munsterhjelm

On Tue, Mar 17, 2009 at 1:19 PM, Dave Ketchum

There has been a lot of guessing - let's see if I can do better, though
Precinct-summable IRV is not reachable. The first counts of top ranks have
to be centrally summed to identify certain losers. Then for each ballot of
such a loser the next-ranked not-yet-lost candidate must be reported.
Have precinct do it, since they have the ballots.
Have had ballot images forwarded so central can do the count.

I agree with you David. And BTW, I also agree with most of what
Kristofer said and in retrospect did not mean that his software idea
was "vaporware" so much as that it would take at least 4 years to be
federally certified at the cost of hundreds of thousands of dollars
just for the certification so that it is "vaporware" only from that
sense of not being available for most states to use for a long time.

I would say that the only way to make it summable is to do it my way,
or at least emulate my way. From what you say, it seems that they make
it "summable" by eliminating all but two candidates and then seeing
which one wins; that is, they run a "fake first round" for all
possible combinations of winner candidates. Then a Plurality count
determines who those two winner candidates are. My claim is then that
of some winner set {X, Y} of two candidates (possible two round
result), X wins iff c[X, Y] > c[Y, X]. That means that their method is
a hackish variant of mine, where the hack is required because they're
stuck with currently certified voting machines.

Summability is a feature of an election method. I suspect that what you
offer fails to pick the winner IRV would, and/or takes too much effort
to deserve bragging.
Condorcet is summable because ALL of the information from a ballot can
be copied into the N*N matrix on first reading of the ballot.
In IRV at the time that the A of A>? is read what the "?" may be does
not matter. When it is determined that A is a loser, then the "?"s on
those ballots will matter.

It fails to pick the winner IRV would, but it picks the winner the
"contingent vote" summability hack picks. The contingent vote is like
this: first do a plurality count. The two candidates that have the
greatest count go to the second round, where the one that's ranked above
the other more often wins. The second round is thus a pairwise
comparison, but it's not Condorcet, since it doesn't check all pairwise
comparisons.

If initial counts were 49A, 48B, and 3other, A or B will win and
all the others can be disposed of together.
If initial counts were 27A, 26B, 25C, and 22D, D loses. Suppose
counts then are 35A, 34B, and 31C, with C losing. If so, have to finish
with A vs B.

My impression was that it was a hack - a way of getting a "summable"
method that can be done using IRV voting machines and that's also at
least slightly IRV-ish.

Post by Kristofer Munsterhjelm

The federal-state voting system certification process is a mess and
the entire voting machine industry is a mess because they use
proprietary standards and so voting system component are not
interoperable, and the flawed design of voting machines makes it
extremely difficult to check to see if the systems are producing
accurate vote counts or not.

To the extent of my knowledge, I agree. I think that having the
machines be engineered around a summable method would help a lot -
then the machines could be, to quote someone whose name escapes me at
the moment, "expensive pencils". A Condorcet counting machine simply
has to do the very simple job of iterating through the ranks; a Range
counting machine just has to turn optical scan configurations into
3/10"). You're left with a small amount of information - the sum of
the array or matrix - that can be made public.

Important goal here is letting voters express their desires, and having
this properly influence who gets elected.
Plurality is weak on the letting.
Approval is better, but gets proper complaints.
Condorcet and score do better, but duel as to which is better.
IRV allows about the same expression as Condorcet, but can deliver
embarrassing results.

For individual ballots, rated ballots probably confer the greatest
freedom. One can simulate a ranked ballot (A: 9, B: 8, C: 7) with or
without ties, and approval style (A: 10, B: 10, C: 0) or Plurality style
as well.

That is, even though the voters may supply ranked or Approval type
ballots (depending on the system in question), all of those could be
stored as rated ballots, which means that in the event of having to
change the voting method, the format doesn't change.

That's for individual ballots. But if the method is summable, one may go
further and ask, what kind of summable data format would provide the
most information? What kind would let one run as many different voting
methods as possible without having to alter the format of what's being
communicated from precincts and summed centrally? One candidate is the
Condorcet matrix. Another is the weighted positional system matrix; or
one may have both, to use methods like "first preference Copeland".

Post by Kristofer Munsterhjelm
if we could only have one change, let that be that rank order machines
use a format that is summable and can be used by a variety of methods.
Condorcet matrices fit (most Condorcet methods only need the matrix).
Weighted positional methods (Borda, etc) can all use another kind of
matrix ({x,y} contains the number equal to how many times candidate x
was voted in yth place). And so on... what you have to decide is what
format to use.

Cycles can occur with Condorcet, so the method must be able to do well
when there is no CW.

Yes. As long as the format is a Condorcet matrix, you may use any method
that does well when there is no CW, as long as that method only required
the Condorcet matrix. For instance, it would be quite easy to shift from
Schulze to MAM/Ranked Pairs, since both work using the Condorcet matrix
alone. In effect, one decouples the calculation (determining the
winners) from the counting (determining what people actually voted), and
one can thus alter one without necessarily having to alter the other.

(By the way, your From address was somewhat strange, purporting to be
from my own ISP, so I used an older one - I hope it's the right one.)
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[Raph Frank]

On Wed, Mar 18, 2009 at 10:26 AM, Kristofer Munsterhjelm

In
effect, one decouples the calculation (determining the winners) from the
counting (determining what people actually voted), and one can thus alter
one without necessarily having to alter the other.

Adb's ballot imaging idea takes this to the extreme. With pattern
recognition software, you could support virtually any voting method.

The "counting" process would just produce a list of numbers
corresponding to each ballot.

In its most simple form, you would just need a pattern recognition
program that can recognise the numbers 0 to 9 and maybe also the
letter X (for "place an X next to your favourite candidate").

As long as the ballots are designed to make this easy, it shouldn't be
that difficult a task. There would be a box provided for each number
that the voter fills in.

I wrote some software that is a basic attempt at this. However, it
only gives 70% ish accuracy.

See:

http://groups.yahoo.com/group/RangeVoting/files/Ballot%20image/

The circles are used to align the image and the black rectange at the
top is used to work out where the top of the ballot is.

I think if there was demand, it should be possible to make this
software much more accurate, since it doesn't have to worry about most
of the complexities of handwriting recognition. It wouldn't have to
separate out letters as each 'box' would only contain one number and
there are only 10 possibilities. Also, since each box would be in a
known position on the page, it would be able to figure out where each
letter is located.
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[James Gilmour]

Raph Frank > Sent: Wednesday, March 18, 2009 12:56 PM

Post by Raph Frank
Adb's ballot imaging idea takes this to the extreme. With
pattern recognition software, you could support virtually any
voting method.
The "counting" process would just produce a list of numbers
corresponding to each ballot.
In its most simple form, you would just need a pattern
recognition program that can recognise the numbers 0 to 9 and
maybe also the letter X (for "place an X next to your
favourite candidate").
As long as the ballots are designed to make this easy, it
shouldn't be that difficult a task. There would be a box
provided for each number that the voter fills in.
I wrote some software that is a basic attempt at this.
However, it only gives 70% ish accuracy.
http://groups.yahoo.com/group/RangeVoting/files/Ballot%20image/
The circles are used to align the image and the black
rectangle at the top is used to work out where the top of the
ballot is.
I think if there was demand, it should be possible to make
this software much more accurate, since it doesn't have to
worry about most of the complexities of handwriting
recognition. It wouldn't have to separate out letters as
each 'box' would only contain one number and there are only
10 possibilities. Also, since each box would be in a known
position on the page, it would be able to figure out where
each letter is located.

I'm afraid there is a little more involved that your description would suggest because real voters do things you might never expect.
But it has all already been done for public elections. Just one example of which I have some knowledge. In May 2007 in Scotland
two different elections were held on the same day. In the MMP elections (Scottish Parliament) the two votes were recorded by "X"s
in separate columns on a combined ballot sheet. In the STV-PR elections (local government - 32 councils) the preferential votes
were recorded by "1, 2, 3" etc in one column, for as many or as few candidates as each voter wished.

The paper ballots from both elections were scanned to produce numerical vote files of the kind you suggest. But the compliance
levels for character recognition were set very high, so many images were queued for evaluation under scrutiny. Those that were
disputed or still uncertain were then queued for adjudication by a Returning Officer, again under full scrutiny. Only then were the
completed numerical files passed to the relevant counting program.

James Gilmour

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[Raph Frank]

Post by James Gilmour
I'm afraid there is a little more involved that your description would suggest because real voters do things you might never expect.
But it has all already been done for public elections. Just one example of which I have some knowledge. In May 2007 in Scotland
two different elections were held on the same day. In the MMP elections (Scottish Parliament) the two votes were recorded by "X"s
in separate columns on a combined ballot sheet. In the STV-PR elections (local government - 32 councils) the preferential votes
were recorded by "1, 2, 3" etc in one column, for as many or as few candidates as each voter wished.

Well, as the software improves, this would be less of a problem.
Also, I think one of the issues in Scotland was poor ballot design
which overloaded the ballot. A better layout might have been two
separate ballots for each person, so it is obvious that they are
separate.

Abd's proposal is that lots of people would take images of the ballots
and each ballot would have an ID number added (after it is taken out
of the ballot box) for easy reference.

There would then be an official provisional file of all the ballots created.

Anyone would be allowed to challenge the official file. You would
effectively give the ballot ID + the correct ballot info for each
disputed image.

The returning officer could then check them using the official ballot images.

If there is still a dispute, it can be brough to court for examination
of the original ballots themselves.

There could be a rule that you can only submit 10 challenges and if
20%+ of them are valid, your limit is increased by 5.
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[James Gilmour]

Raph Frank > Sent: Wednesday, March 18, 2009 3:20 PM

Post by Raph Frank
Well, as the software improves, this would be less of a
problem.

I'm afraid you have misunderstood (or maybe I didn't explain it clearly). It is not a software issue - it is a compliance issue.
No matter what software you use to "read" the images, the Returning Officers will always have to decide the level of compliance for
automatic acceptance. Many more ballot paper images could be processed completely automatically if the compliance level were
reduced, even a little. But such is the distrust of "black boxes" that the ROs in Scotland asked for the compliance levels to be
set quite high. Hence the "symbol correction" queue. The "adjudication queue" is quite separate and will always exist.

Post by Raph Frank
Also, I think one of the issues in Scotland was poor
ballot design which overloaded the ballot.

There's lots I could write about this, but I don't have time right now. The real problem was with the MMP elections. The large
processing queues and delays resulted from the need for adjudication on anything that did not conform, including a ballot sheet with
only one vote recorded on it instead of the expected two.

If you want to know more about this, see:
Rejected Ballot Papers in the Scottish Elections 2007
http://www.epop07.com/papers/Gilmour-Pre-Conf-Paper-31Aug07.pdf

Post by Raph Frank
A better layout
might have been two separate ballots for each person, so it
is obvious that they are separate.

Separate ballot papers were used for the two MMP votes in the elections in 1999 and 2003. The combined ballot sheet (following New
Zealand) was introduced in 2007 to address some very large problems in voter understanding of how MMP really works. For more on
that, see the report of the Arbuthnott Commission:
http://www.scotlandoffice.gov.uk/scotlandoffice/files/Final%20version%20of%20report.pdf

Post by Raph Frank
Abd's proposal is that lots of people would take images of
the ballots and each ballot would have an ID number added
(after it is taken out of the ballot box) for easy reference.

All ballot papers in the UK have a unique number printed on the back. For electronic processing, they also have a unique barcode on
the back that goes with the scanned image. The system is designed, both paper and electronic, so that no-one can see, at the same
time, both the face and reverse of a ballot paper or an image of a ballot paper. You need a Court Order for authority to look at
both the face and reverse of the ballot papers, and that will be granted only in cases where there is good evidence for fraud to be
suspected.

James Gilmour


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[Raph Frank]

Post by James Gilmour
Raph Frank > Sent: Wednesday, March 18, 2009 3:20 PM

Post by Raph Frank
Well, as the software improves, this would be less of a
problem.

I'm afraid you have misunderstood (or maybe I didn't explain it clearly). It is not a software issue - it is a compliance issue.
No matter what software you use to "read" the images, the Returning Officers will always have to decide the level of compliance for
automatic acceptance.

By compliance, do you mean the confidence level that the software outputs?

Multiple independent images, processed by different people help with
this issue. You would only need to check ballots where there is
disagreement.
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[James Gilmour]

Raph Frank > Sent: Wednesday, March 18, 2009 5:54 PM

Post by Raph Frank

Post by James Gilmour
I'm afraid you have misunderstood (or maybe I didn't explain it
clearly). It is not a software issue - it is a compliance issue. No
matter what software you use to "read" the images, the Returning
Officers will always have to decide the level of compliance for
automatic acceptance.

By compliance, do you mean the confidence level that the
software outputs?

I do not know how the DRS software works, so I cannot answer the question as asked. But as I understand, some form of "intelligent"
OCR is used to "read" the image to produce the vote vector for each ballot paper. The system can be set to accept or reject various
forms of the "same" vote mark. This is, for example, an unbelievably large number of ways of marking a "1" in a square in the
voting column!! What angle away from vertical is acceptable? What degree of curl in the pencil stroke is acceptable? Does it have
an up-stroke so that it might confused with a "7"? etc, etc, etc. You have to see the images (hundreds of them) to appreciate the
variation in what is actually done by voters. For the 2007 elections, an image was queued for evaluation if even the tiniest part
of a vote mark ("X" or a number, depending on the election) went over the border into the next box. Also queued for evaluation
were all ballot papers that had ANY additional marks at all anywhere on the face of the paper.

As I understand it, there are settable parameters in the system that could be set to accept or reject all of the variations
described above, and many more. The compliance requirements were set high because when I and many others looked at the symbol
images queued for evaluation, we said it was obvious which most of them were. But they had been queued because, in some way, they
did not comply with the parameters set and agreed by the Returning Officers.

Post by Raph Frank
Multiple independent images, processed by different people
help with this issue. You would only need to check ballots
where there is disagreement.

I am not sure what you meant here, but if there was any disagreement about the "symbol correction" at the evaluation stage, the
image was queued for adjudication by a Returning Officer. There were comparatively few queued for that reason. But there were very
large numbers queued for adjudication for other reasons, so that the candidates and their agents would be happy with the decisions.

The system used in 2007 was non-heuristic, but there was a heuristic version available that would "learn" from the "symbol
corrections" at the evaluation stage and so progressively queue fewer and fewer images for evaluation. But that would have been a
"black box" step too far, at least on that occasion which was the first time any of the countries in the UK had used electronic
counting for ALL its elections.

James

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[Raph Frank]

I uploaded the example ballot .pdf file that the code uses to
http://groups.yahoo.com/group/RangeVoting/files/Ballot%20image/temp_ballot.pdf

Also, some intermediate files from processing the image0001.pnp file.

This is after determining the alignment points:
http://groups.yahoo.com/group/RangeVoting/files/Ballot%20image/regen_plus.bmp

These are the images of each extracted box (after rescaling etc):

http://groups.yahoo.com/group/RangeVoting/files/Ballot%20image/small_0.bmp
http://groups.yahoo.com/group/RangeVoting/files/Ballot%20image/small_1.bmp
http://groups.yahoo.com/group/RangeVoting/files/Ballot%20image/small_2.bmp
http://groups.yahoo.com/group/RangeVoting/files/Ballot%20image/small_3.bmp
http://groups.yahoo.com/group/RangeVoting/files/Ballot%20image/small_4.bmp
http://groups.yahoo.com/group/RangeVoting/files/Ballot%20image/small_5.bmp
http://groups.yahoo.com/group/RangeVoting/files/Ballot%20image/small_6.bmp
http://groups.yahoo.com/group/RangeVoting/files/Ballot%20image/small_7.bmp

These are the same boxes after processing
http://groups.yahoo.com/group/RangeVoting/files/Ballot%20image/short_0.bmp
http://groups.yahoo.com/group/RangeVoting/files/Ballot%20image/short_1.bmp
http://groups.yahoo.com/group/RangeVoting/files/Ballot%20image/short_2.bmp
http://groups.yahoo.com/group/RangeVoting/files/Ballot%20image/short_3.bmp
http://groups.yahoo.com/group/RangeVoting/files/Ballot%20image/short_4.bmp
http://groups.yahoo.com/group/RangeVoting/files/Ballot%20image/short_5.bmp
http://groups.yahoo.com/group/RangeVoting/files/Ballot%20image/short_6.bmp
http://groups.yahoo.com/group/RangeVoting/files/Ballot%20image/short_7.bmp

It gets 7 of the 8 correct. The only error is the blank box (5).

The main thing, atm, that causes errors is the boxes themselves, as
the processing interprets them as part of the handwriting. I think
that shouldn't be to hard to fix, but would require that the extracted
boxes are processed to find out exactly where their boundary lines
are. Currently, it is open loop, it is assumed that the alignment
points are determined exactly.

With that, it could end up with 85%+ (at least with my handwriting :) ).
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[Kristofer Munsterhjelm]

Post by Raph Frank
I uploaded the example ballot .pdf file that the code uses to
http://groups.yahoo.com/group/RangeVoting/files/Ballot%20image/temp_ballot.pdf
Also, some intermediate files from processing the image0001.pnp file.
http://groups.yahoo.com/group/RangeVoting/files/Ballot%20image/regen_plus.bmp
http://groups.yahoo.com/group/RangeVoting/files/Ballot%20image/small_0.bmp
http://groups.yahoo.com/group/RangeVoting/files/Ballot%20image/small_1.bmp
http://groups.yahoo.com/group/RangeVoting/files/Ballot%20image/small_2.bmp
http://groups.yahoo.com/group/RangeVoting/files/Ballot%20image/small_3.bmp
http://groups.yahoo.com/group/RangeVoting/files/Ballot%20image/small_4.bmp
http://groups.yahoo.com/group/RangeVoting/files/Ballot%20image/small_5.bmp
http://groups.yahoo.com/group/RangeVoting/files/Ballot%20image/small_6.bmp
http://groups.yahoo.com/group/RangeVoting/files/Ballot%20image/small_7.bmp
These are the same boxes after processing
http://groups.yahoo.com/group/RangeVoting/files/Ballot%20image/short_0.bmp
http://groups.yahoo.com/group/RangeVoting/files/Ballot%20image/short_1.bmp
http://groups.yahoo.com/group/RangeVoting/files/Ballot%20image/short_2.bmp
http://groups.yahoo.com/group/RangeVoting/files/Ballot%20image/short_3.bmp
http://groups.yahoo.com/group/RangeVoting/files/Ballot%20image/short_4.bmp
http://groups.yahoo.com/group/RangeVoting/files/Ballot%20image/short_5.bmp
http://groups.yahoo.com/group/RangeVoting/files/Ballot%20image/short_6.bmp
http://groups.yahoo.com/group/RangeVoting/files/Ballot%20image/short_7.bmp
It gets 7 of the 8 correct. The only error is the blank box (5).
The main thing, atm, that causes errors is the boxes themselves, as
the processing interprets them as part of the handwriting. I think
that shouldn't be to hard to fix, but would require that the extracted
boxes are processed to find out exactly where their boundary lines
are. Currently, it is open loop, it is assumed that the alignment
points are determined exactly.
With that, it could end up with 85%+ (at least with my handwriting :) ).

One would probably use a neural net type algorithm to determine the
digit in question. As for the boxes, perhaps one could use a Hough
transform (see http://en.wikipedia.org/wiki/Hough_transform) to find
lines, then align the pictures according to those lines?

Also, I am not a member of RangeVoting, so I can't see those pictures.
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[Terry Bouricius]

Indeed, pixel scanning voting technology that captures complete ballot
images that can be interpreted using standard form-reading software allows
for ANY improved voting method AND increases election integrity by having
a redundant paper and machine record of every vote (making fraud extremely
difficult, since TWO records would need to be falsified). And this is not
a wish for the future, but happening right now. Several current election
administration companies (mainly running union elections) use such a
system currently, and at least one voting machine vendor (Avante, which
just won a huge contract to supply voting machines to the Philippines) has
such a system already federally tested in the U.S.

Terry Bouricius
----- Original Message -----
From: "Raph Frank" <***@gmail.com>
To: "Kristofer Munsterhjelm" <km-***@broadpark.no>
Cc: "Dave Ketchum" <***@clarityconnect.com>; "EM"
<election-***@lists.electorama.com>
Sent: Wednesday, March 18, 2009 8:55 AM
Subject: Re: [EM] IRV proponents figure out how to make IRV
precinct-summable


On Wed, Mar 18, 2009 at 10:26 AM, Kristofer Munsterhjelm

In
effect, one decouples the calculation (determining the winners) from the
counting (determining what people actually voted), and one can thus alter
one without necessarily having to alter the other.

Adb's ballot imaging idea takes this to the extreme. With pattern
recognition software, you could support virtually any voting method.

The "counting" process would just produce a list of numbers
corresponding to each ballot.

In its most simple form, you would just need a pattern recognition
program that can recognise the numbers 0 to 9 and maybe also the
letter X (for "place an X next to your favourite candidate").

As long as the ballots are designed to make this easy, it shouldn't be
that difficult a task. There would be a box provided for each number
that the voter fills in.

I wrote some software that is a basic attempt at this. However, it
only gives 70% ish accuracy.

See:

http://groups.yahoo.com/group/RangeVoting/files/Ballot%20image/

The circles are used to align the image and the black rectange at the
top is used to work out where the top of the ballot is.

I think if there was demand, it should be possible to make this
software much more accurate, since it doesn't have to worry about most
of the complexities of handwriting recognition. It wouldn't have to
separate out letters as each 'box' would only contain one number and
there are only 10 possibilities. Also, since each box would be in a
known position on the page, it would be able to figure out where each
letter is located.
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[Kristofer Munsterhjelm]

Post by Raph Frank
On Wed, Mar 18, 2009 at 10:26 AM, Kristofer Munsterhjelm

In
effect, one decouples the calculation (determining the winners) from the
counting (determining what people actually voted), and one can thus alter
one without necessarily having to alter the other.

Adb's ballot imaging idea takes this to the extreme. With pattern
recognition software, you could support virtually any voting method.
The "counting" process would just produce a list of numbers
corresponding to each ballot.
In its most simple form, you would just need a pattern recognition
program that can recognise the numbers 0 to 9 and maybe also the
letter X (for "place an X next to your favourite candidate").
As long as the ballots are designed to make this easy, it shouldn't be
that difficult a task. There would be a box provided for each number
that the voter fills in.
I wrote some software that is a basic attempt at this. However, it
only gives 70% ish accuracy.
http://groups.yahoo.com/group/RangeVoting/files/Ballot%20image/
The circles are used to align the image and the black rectange at the
top is used to work out where the top of the ballot is.
I think if there was demand, it should be possible to make this
software much more accurate, since it doesn't have to worry about most
of the complexities of handwriting recognition. It wouldn't have to
separate out letters as each 'box' would only contain one number and
there are only 10 possibilities. Also, since each box would be in a
known position on the page, it would be able to figure out where each
letter is located.

Let's look at this in a hierarchical manner. Doing so, we get:

level 0: raw images of the ballots
level 1: parsed ballot data, not summable
level 2: parsed and counted ballots, some summable format (if possible)
level 3: social compromise ballot (social ordering or rating)
level 4: winner/s

Level 4 applies to all methods that determine one or more winners.
Practically all election methods do this. There is only one level 4
result - a set consisting of the winners according to the method.

Level 3 applies to those that produce either a social ordering or an
"aggregate rated ballot" (like a social ordering, but with rating
instead of ranking). Most methods can be extended to produce a social
ordering. For instance, all elimination-based methods can do this by
noting the order of elimination, then reversing that (first eliminated
is ranked last). As with level 4, there is only one instance of level 3
data - that which is produced by the final calculation.

Level 2 applies to all summable methods. There may be many instances of
level 2 data, but by the definition of summability, the chunks are
limited in size by a polynomial function of the number of candidates.

Levels 1 and 0 apply to all methods, except possibly those that rely on
sortition (where the order of the ballots matter). In the worst case,
all voters vote in a different order (and with different ratings, if
it's a rated system).

Define lg(x) = binary logarithm of x, also nC = number of candidates, nV
= number of voters.

For level 1, this produces, for a ranked system, min(nC! * lg(nV),
lg(nC!) * nV) ballots, and for a rated system where the maximum rating
is y and the minimum rating is x (in steps of 1), min(lg(nV) *
(y+1-x)^nC, lg(y+1-x) * nC * nV). The point is that either one has a
format of the type "for each possible rank/rating, list how many people
voted this way" (thus requiring lg(nV) for the digits), or "for each
person, list how he voted" (thus requiring lg of [the number of unique
votes] for the digits).
For level 0, each voter may trivially make a unique mark somewhere so
that all the ballots are unique. Thus the worst case is simply nV.

-

To get back to what you're saying; yes, it's possible to store raw
ballot data. For a ranked ballot system and modern storage, level 1 data
may even be storable for a United States-wide election with 13
candidates. The eligible US population is 2e8 (roughly speaking), so
lg(13!) * 2e8 = 6.5 billion bits = 775 MB.

Level 0 data is tougher still, but could be done. The problem is that in
the worst case, each ballot may be unique. This counts against us both
in storing and in vote-buying cases (since a voter might mark the ballot
in some special way to identify himself to the buyer). Obviously, one
would need a lot of space if the entire ballot is to be imaged, but this
may be fixed to some extent by only imaging the boxes where the voters
write the numbers that constitute their rank or rating.

In any case, what appears, and what makes the summability criterion
useful, is that shipping around level 2 data is much easier than to do
so with level 1 or level 0 data. The whole point of a voting system
itself is to do data reduction (hopefully consistent with the qualities
the public desire of a voting system) - from level 0 to level 3 or 4,
and further to representation - so that one may deal with the reduced
data instead of the enormous amount that is the people's opinion. If one
could deal with the enormous amount, there would be little point, and
one could just have a direct democracy.
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[Kristofer Munsterhjelm]

Post by Kristofer Munsterhjelm
It fails to pick the winner IRV would, but it picks the winner the
"contingent vote" summability hack picks. The contingent vote is like
this: first do a plurality count. The two candidates that have the
greatest count go to the second round, where the one that's ranked
above the other more often wins. The second round is thus a pairwise
comparison, but it's not Condorcet, since it doesn't check all
pairwise comparisons.

But I do not see summable here, for that would mean NOT going back to
the precincts for the second round.

As stated, it's not summable. But note that the second round, which is
determined by the Plurality count, consists of a pairwise comparison.
Thus, one can make the method summable by simply storing the information
required to simulate any one-on-one runoff -- in other words, by having
a Condorcet matrix. Since Condorcet is not mutually exclusive with
summability, we know Condorcet matrices can be summed - so that part is
summable. We also know that Plurality counts are summable - if A gets X
votes in district 1 and Y votes in district 2, A got X+Y votes in these
districts combined.

Again, the election method better get decided on before the election, so
that the voters can be told the rules and thus be able to express their
Condorcet: A=B is fine for about equals; A>B or A<B ranking for
different liking, but amount of difference is neither needed nor
expressible.
IRV: like above, except A=B not permitted, for counting would not
know what to do when A=B must be deciphered as top ranks.
score: ratings must be decided - for A>B>C, obvious to rate A high
and C low, but where to place B to get maximum or minimum difference
between A and B or between B and C is difficult.

I'm not sure about IRV - has anyone devised an STV variant that handles
equal rank? If not, then you're right - again, I'm not sure.

From what I've seen of voting equipment, most limitations seem to be in
the name of expediency. For instance, SF's RCV three-rank method keeps
voters from ranking more than three candidates - probably to accomodate
existing equipment.

What limitations may exist (such as your IRV example) may be handled by
having a voting machine that permits all ranking types (full, truncated,
equal rank), then having parameters that limit according to what kind of
voting system is being used in the back end (e.g no equal rank).

Post by Kristofer Munsterhjelm
My impression was that it was a hack - a way of getting a "summable"
method that can be done using IRV voting machines and that's also at
least slightly IRV-ish.

Sounds like it was neither summable nor truly IRV.

It is in theory possible to make it summable - see above. The method
they did use seems not to be, though - as far as I could see, they
checked, for all possible virtual runoffs (set by enforcing A and B as
winners in the first round), whether A or B won. Such a binary check is
summable only if the results are the same in both districts - but when
they're different, one runs into trouble. Consider this, for instance:

District 1 X>Y: 1000, Y>X: 990 X beats Y
District 2 X>Y: 1, Y>X: 2 Y beats X
-------------------------------------------------
Summed result X beats Y

but also

District 1 X>Y: 1000, Y>X: 990 X beats Y
District 2 X>Y: 1000, Y>X: 2000 Y beats X
-------------------------------------------------
Summed result Y beats X

In both instances, X beats Y in the first district, and Y beats X in the
second district, but the summed result is different for the two cases.
Thus I think that they would have to store the entire Condorcet matrix
(numbers of voters, not just who won) in order to be summable. If they
did, then they're summable, but if they didn't, they aren't.

(This contradicts what I said earlier, where I claimed they were
summable because they stored the entire CM. A rereading seems to say
they are only storing who won the virtual runoff, but again, I could be
wrong.)

It is, as you say, most definitely not IRV.

Post by Kristofer Munsterhjelm
For individual ballots, rated ballots probably confer the greatest
freedom. One can simulate a ranked ballot (A: 9, B: 8, C: 7) with or
without ties, and approval style (A: 10, B: 10, C: 0) or Plurality
style as well.

Disagreed as to freedom - rating does permit more detail - but then
demands that the voter decide how to express it.

I mean freedom as a data format. A rated vote data format can emulate a
ranked vote format, as well as an approval-style data format.

Post by Kristofer Munsterhjelm
That is, even though the voters may supply ranked or Approval type
ballots (depending on the system in question), all of those could be
stored as rated ballots, which means that in the event of having to
change the voting method, the format doesn't change.

If the voter thinks and votes Approval, the counter cannot know how the
voter would have expressed Condorcet or score voting.

That is correct. One may "downconvert" but not "upconvert".

There is one exception: ranked ballot to Approval-style. The ranked
ballot contains no information about where to put the cutoff. One could
also generalize this exception to rated-to-ranked, saying that A: 4.99
B: 4.98 should be A = B, but A: 49, B: 48 should be A > B. If this
problem is significant, it would destroy the freedom argument above.

Post by Kristofer Munsterhjelm
That's for individual ballots. But if the method is summable, one may
go further and ask, what kind of summable data format would provide
the most information? What kind would let one run as many different
voting methods as possible without having to alter the format of
what's being communicated from precincts and summed centrally? One
candidate is the Condorcet matrix. Another is the weighted positional
system matrix; or one may have both, to use methods like "first
preference Copeland".

You seem to be thinking of our debates in EM or Rangevoting. For an
actual election I claim above that the method BETTER get decided before
the election, and the data format and counting operations BETTER fit
that method.

Having a common format would let states tell manufacturers to make
machines able to read or write to that format before they're completely
sure as to which method using that format is to be used. For instance,
say a state decides to use Condorcet. It's not sure as to what kind yet,
though, but now it can order voting machines that add to Condorcet
matrices. Some time later, but before the election, they pick (say)
Schulze. The time of the election comes and they find the winner based
on the Condorcet matrix data, the actual Condorcet counting part of the
machines having been thoroughly tested.

Is that unrealistic?

Again, the method better get decided before the election. That two
methods use the same matrix does not excuse allowing for method debates
after the election among the various candidates claiming to have won.

The method used should be the method that counts, yes; arguing over
other methods would not affect the outcome, except inasfar as they may
point to problems with the method itself. In that respect, it's both a
benefit and a disadvantage: "problems with the method" might be defined
by the people as something like "vulnerable to vote splitting" (that's
the benefit), but might also be defined by those in power as something
like "too competitive" (that's the disadvantage).

Post by Kristofer Munsterhjelm
(By the way, your From address was somewhat strange, purporting to be
from my own ISP, so I used an older one - I hope it's the right one.)

Do not understand these words, but what came as cc was correct.

Simply put, the From: of your previous mail (and of this one, too) was
"***@broadpark.no". Broadpark.no is where my own
mail account resides.
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[Brian Olson]

Post by Kristofer Munsterhjelm

Again, the election method better get decided on before the
election, so that the voters can be told the rules and thus be able
to express their thoughts to whatever extent they choose within
Condorcet: A=B is fine for about equals; A>B or A<B ranking
for different liking, but amount of difference is neither needed
nor expressible.
IRV: like above, except A=B not permitted, for counting would
not know what to do when A=B must be deciphered as top ranks.
score: ratings must be decided - for A>B>C, obvious to rate A
high and C low, but where to place B to get maximum or minimum
difference between A and B or between B and C is difficult.

I'm not sure about IRV - has anyone devised an STV variant that
handles equal rank? If not, then you're right - again, I'm not sure.
From what I've seen of voting equipment, most limitations seem to be
in the name of expediency. For instance, SF's RCV three-rank method
keeps voters from ranking more than three candidates - probably to
accomodate existing equipment.
What limitations may exist (such as your IRV example) may be handled
by having a voting machine that permits all ranking types (full,
truncated, equal rank), then having parameters that limit according
to what kind of voting system is being used in the back end (e.g no
equal rank).

All of my implementations of election methods in software allow for
equal rankings. In IRV or STV they cast a 1/N vote for each of N tied-
rank active choices. (If I were to vote for A and B in some round, I'd
cast 1/2 vote for each, but if one got eliminated, I would cast a full
vote for the remaining one in the next round.)
If you like Java, peek at this:
http://code.google.com/p/voteutil/source/browse/trunk/java/org/bolson/vote/IRV.java

I would also like to note to Raph that hosting files on the yahoo
groups is making them not viewable to me, because I don't feel like
jumping through yahoo's hoops right now.

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[Raph Frank]

I would also like to note to Raph that hosting files on the yahoo groups is
making them not viewable to me, because I don't feel like jumping through
yahoo's hoops right now.

Sorry thought 'files' was open to public view.

I have moved the files to:

http://prydwen.net/scanned_files/ballot.html
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[Dave Ketchum]

Post by Kristofer Munsterhjelm

Post by Kristofer Munsterhjelm
(By the way, your From address was somewhat strange, purporting to
be from my own ISP, so I used an older one - I hope it's the right
one.)

Do not understand these words, but what came as cc was correct.

Simply put, the From: of your previous mail (and of this one, too)
own mail account resides.

It was the header that flunked on my new computer.

Thanks to Kristofer for bugging me til I understood and fixed.

[Kristofer Munsterhjelm]

Post by Kristofer Munsterhjelm
As stated, it's not summable. But note that the second round, which is
determined by the Plurality count, consists of a pairwise comparison.
Thus, one can make the method summable by simply storing the
information required to simulate any one-on-one runoff -- in other
words, by having a Condorcet matrix. Since Condorcet is not mutually
exclusive with summability, we know Condorcet matrices can be summed -
so that part is summable. We also know that Plurality counts are
summable - if A gets X votes in district 1 and Y votes in district 2,
A got X+Y votes in these districts combined.

Agreed that Condorcet and Plurality, and even Approval, are summable.
Condorcet will count A>B, A>B, A>C, A>C, B>C, and C>B into the N*N
matrix.
IRV will only see A>? and A>? until and unless A losing exposes
what remains (B>? or C>?).
True that ballot images could be forwarded, but that does not really
make summable claimable.

Agreed (in turn) that forwarding ballot images doesn't make a method
summable, since otherwise, any method that doesn't care about the order
of the ballots would be "summable".

Also, IRV, in the general case, is not summable. However, what we're
talking about is the contingent vote, an "instant top-two runoff", which
is what the IRV proponents figured out how to make precinct summable (or
thought they had figured out how to make precinct summable). It agrees
with IRV if the number of candidates <= 3.

The contingent vote first counts plurality votes for the various
candidates, as top-two runoff does. Then, again as in top-two runoff,
the two "winners", Plurality wise, go to the next round. The difference
is that the contingent vote uses the same rank ballots for the second
round as for the first, only with all non-winners eliminated, whereas
true TTR has a separate second round.

Let's have a concrete example of how the contingent vote works, and why
my approach to it is summable.

District 1: 100: A > B > C
98: B > C > A
27: C > A > B

District 2: 104: C > B > A
121: C > A > B
50: A > B > C
25: B > A > C

Combined: 104: C > B > A
150: A > B > C
148: C > A > B
98: B > C > A
25: B > A > C

For the combined ballot, first do a Plurality count to see who advances.
Note that this Plurality count is what makes contingent vote equal to
IRV for number of candidates = 3, since preserving the top two is equal
to eliminating the last candidate.

Combined, plurality: 104 C, 150 A, 148 C, 98 B, 25 B
hence: 252 C, 150 A, 123 B

So C and A move to the second round.

Eliminating B, we get
104: C > A
150: A > C
148: C > A
98: C > A
25: A > C
summing up,
350: C > A
175: A > C

So C wins.

Let's look at the combined Condorcet matrix. It is

A B C beats
A --- 227 350
B 298 --- 252
C 175 273 ---

Here you can see that the data we're looking for is "C beats A" and "A
beats C". Since there are only two candidates remaining from the first
round, the second round will be an one-on-one, which is the kind of
contest the Condorcet matrix stores information about. If C beats A more
often than A beats C, C is the winner. Incidentally, this shows that the
contingent vote passes Condorcet loser.

But let's do it again, with only the summable information about each
district (that is, the plurality count and the Condorcet matrix).

District 1:
Plurality count: 100 A, 98 B, 27 C

Condorcet matrix: A B C beats
A --- 98 125
B 127 --- 27
C 100 198 ---

District 2:
Plurality count: 50 A, 25 B, 225 C

Condorcet matrix: A B C beats
A --- 129 225
B 171 --- 225
C 75 75 ---

Let's sum this all up:
Plurality count: 150 A, 123 B, 252 C

Condorcet matrix: A B C beats
A --- 227 350
B 298 --- 252
C 175 273 ---

And run the election method again:
First "round": greatest two are A (150) and C (252)
So A and C go to the second "round".
Second "round": A>C by 175, C>A by 350, so C wins.

There you go, the contingent vote is summable.

Post by Kristofer Munsterhjelm
I'm not sure about IRV - has anyone devised an STV variant that
handles equal rank? If not, then you're right - again, I'm not sure.

Brian claims, and I cannot disprove, that IRV can be stretched to
tolerate equal rank - questionable whether it would be worth the expense
for real elections.

There are two ways to handle equal rank, in theory, for a weighted
positional method. Plurality is just a weighted positional method with
the weights (1, 0, 0, ..., 0). The first is "whole", which means that if
you rank A = B > C, A and B has the same score, which is the same as A
in A > C. For plurality, that would turn it into Approval. The second is
"fractional", which means that the sum of the score for all ranked
candidates in a certain rank is the same, no matter how many you ranked.
For instance, for Plurality, ranking A = B > C would give half a point
to A and B (so that the sum is 1), and none to C, whereas ranking A > B

C would give a full point to A and none to B or C.

Elimination would work the same way however equal rank would be treated.
If you vote A = B > C and A is eliminated, then for the next round, your
vote is B > C.

Assuming the voting machines can handle the input, where would the
expense lie in adding this support? It seems to be more a question of
whether the resulting system would be "IRV" or not... unless the expense
would be in "handling the input", but if you have a machine that can
handle A > B > C > D > E .. > Z, upgrading it to handle A = B = C > D >
E ... doesn't seem to be that expensive a change.

Post by Kristofer Munsterhjelm
From what I've seen of voting equipment, most limitations seem to be
in the name of expediency. For instance, SF's RCV three-rank method
keeps voters from ranking more than three candidates - probably to
accomodate existing equipment.

Some ways of providing for more ranks significantly burden
equipment design.
Providing for 2 ranks is essential to deserve claim as to ranks
existing; 3 helps some; more than 3 helps real voters little.

One may then ask, how many ranks are required to break Duverger's Law?
Unfortunately, I don't know the answer.

Post by Kristofer Munsterhjelm
What limitations may exist (such as your IRV example) may be handled
by having a voting machine that permits all ranking types (full,
truncated, equal rank), then having parameters that limit according to
what kind of voting system is being used in the back end (e.g no equal
rank).

Sounds like building in expensive complications.
Doing the specialization in software could be affordable.

There's a tradeoff at this point. Having a generalized machine lets you
build many that are all the same, so that you gain benefits of scale.
However, the generalized machine is more expensive because you can't cut
away what you don't need.

Post by Kristofer Munsterhjelm
It is in theory possible to make it summable - see above. The method
they did use seems not to be, though - as far as I could see, they
checked, for all possible virtual runoffs (set by enforcing A and B as
winners in the first round), whether A or B won. Such a binary check
is summable only if the results are the same in both districts - but
when they're different, one runs into trouble. Consider this, for
District 1 X>Y: 1000, Y>X: 990 X beats Y
District 2 X>Y: 1, Y>X: 2 Y beats X
-------------------------------------------------
Summed result X beats Y
but also
District 1 X>Y: 1000, Y>X: 990 X beats Y
District 2 X>Y: 1000, Y>X: 2000 Y beats X
-------------------------------------------------
Summed result Y beats X
In both instances, X beats Y in the first district, and Y beats X in
the second district, but the summed result is different for the two
cases. Thus I think that they would have to store the entire Condorcet
matrix (numbers of voters, not just who won) in order to be summable.
If they did, then they're summable, but if they didn't, they aren't.

Condorcet cares not as to number of voters - for it simply sum the
matrices.

If nobody equal-ranks, then (A beats B) + (B beats A) = number of
voters. Apart from that, you're right, Condorcet doesn't care. What I
showed was that if they (the IRV proponents) tried to use only binary
arrays instead of integer arrays for their kinda-Condorcet matrices,
they would fail, because there's not enough information there. A
Condorcet matrix has to be integer (or even more fine grained, e.g for
CWP), even when that matrix is only to be used for determining the
winner of the contingent vote.

Post by Kristofer Munsterhjelm
I mean freedom as a data format. A rated vote data format can emulate
a ranked vote format, as well as an approval-style data format.

Saying freedom reminds me of something we sometimes ignore - how much
complication do we burden voters with.

Voting is already irrational from a utilitarian point of view - your
chance of affecting the outcome is way too small for it to be worth
bothering to vote, let alone consider the issues to make an informed
decision. Yet we vote anyway.

That muddies the waters, because we can't use standard
utilitarian/economic theory to find out how much complication is too
much. Perhaps people wouldn't bother with anything more than Approval,
but that seems wrong (since people rate and rank things all the time).
So, how much is too much? I don't know.

Of course, the user interface should be good, but that's a separate
issue. I don't particularly like general purpose direct electronic
machines, so the "user interface" may be entirely transparent - put the
appropriate number in the box next to the candidate (for each
candidate), then at some later time, OCR reads off the numbers to parse
the ballot.

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[Dave Ketchum]

Post by Kristofer Munsterhjelm

Post by Kristofer Munsterhjelm
As stated, it's not summable. But note that the second round,
which is determined by the Plurality count, consists of a pairwise
comparison. Thus, one can make the method summable by simply
storing the information required to simulate any one-on-one runoff
-- in other words, by having a Condorcet matrix. Since Condorcet
is not mutually exclusive with summability, we know Condorcet
matrices can be summed - so that part is summable. We also know
that Plurality counts are summable - if A gets X votes in district
1 and Y votes in district 2, A got X+Y votes in these districts
combined.

Agreed that Condorcet and Plurality, and even Approval, are summable.
Condorcet will count A>B, A>B, A>C, A>C, B>C, and C>B into the
N*N matrix.
IRV will only see A>? and A>? until and unless A losing exposes
what remains (B>? or C>?).
True that ballot images could be forwarded, but that does not
really make summable claimable.

Agreed (in turn) that forwarding ballot images doesn't make a method
summable, since otherwise, any method that doesn't care about the
order of the ballots would be "summable".
Also, IRV, in the general case, is not summable. However, what we're
talking about is the contingent vote, an "instant top-two runoff",
which is what the IRV proponents figured out how to make precinct
summable (or thought they had figured out how to make precinct
summable). It agrees with IRV if the number of candidates <= 3.
The contingent vote first counts plurality votes for the various
candidates, as top-two runoff does. Then, again as in top-two
runoff, the two "winners", Plurality wise, go to the next round. The
difference is that the contingent vote uses the same rank ballots
for the second round as for the first, only with all non-winners
eliminated, whereas true TTR has a separate second round.

Let's see:
Plurality and Condorcet look at the ballots ONE time, and never
go back. Does summable require this - never going back to the
ballots, or to the voters, more times?
TTR needs to go back only if the top two were near to a tie -
IRV could do the same.
For TTR the second round presumably always finishes it; get
near enough to a tie and IRV could need more rounds - but they do not
mean extra effort from the voters.

Post by Kristofer Munsterhjelm
Let's have a concrete example of how the contingent vote works, and
why my approach to it is summable.
District 1: 100: A > B > C
98: B > C > A
27: C > A > B
District 2: 104: C > B > A
121: C > A > B
50: A > B > C
25: B > A > C
Combined: 104: C > B > A
150: A > B > C
148: C > A > B
98: B > C > A
25: B > A > C
For the combined ballot, first do a Plurality count to see who
advances. Note that this Plurality count is what makes contingent
vote equal to IRV for number of candidates = 3, since preserving the
top two is equal to eliminating the last candidate.
Combined, plurality: 104 C, 150 A, 148 C, 98 B, 25 B
hence: 252 C, 150 A, 123 B
So C and A move to the second round.
Eliminating B, we get
104: C > A
150: A > C
148: C > A
98: C > A
25: A > C
summing up,
350: C > A
175: A > C
So C wins.
Let's look at the combined Condorcet matrix. It is
A B C beats
A --- 227 350
B 298 --- 252
C 175 273 ---
Here you can see that the data we're looking for is "C beats A" and
"A beats C". Since there are only two candidates remaining from the
first round, the second round will be an one-on-one, which is the
kind of contest the Condorcet matrix stores information about. If C
beats A more often than A beats C, C is the winner. Incidentally,
this shows that the contingent vote passes Condorcet loser.
But let's do it again, with only the summable information about each
district (that is, the plurality count and the Condorcet matrix).
Plurality count: 100 A, 98 B, 27 C
Condorcet matrix: A B C beats
A --- 98 125
B 127 --- 27
C 100 198 ---
Plurality count: 50 A, 25 B, 225 C
Condorcet matrix: A B C beats
A --- 129 225
B 171 --- 225
C 75 75 ---
Plurality count: 150 A, 123 B, 252 C
Condorcet matrix: A B C beats
A --- 227 350
B 298 --- 252
C 175 273 ---
First "round": greatest two are A (150) and C (252)
So A and C go to the second "round".
Second "round": A>C by 175, C>A by 350, so C wins.
There you go, the contingent vote is summable.

Not clear why the two districts were even mentioned.

Since Condorcet was mentioned, might make sense to include a cycle and
see how much this complicates life.

As I say above, what qualifies as summable?

Post by Kristofer Munsterhjelm

Post by Kristofer Munsterhjelm
I'm not sure about IRV - has anyone devised an STV variant that
handles equal rank? If not, then you're right - again, I'm not sure.

Brian claims, and I cannot disprove, that IRV can be stretched to
tolerate equal rank - questionable whether it would be worth the
expense for real elections.

There are two ways to handle equal rank, in theory, for a weighted
positional method. Plurality is just a weighted positional method
with the weights (1, 0, 0, ..., 0). The first is "whole", which
means that if you rank A = B > C, A and B has the same score, which
is the same as A in A > C. For plurality, that would turn it into
Approval. The second is "fractional", which means that the sum of
the score for all ranked candidates in a certain rank is the same,
no matter how many you ranked. For instance, for Plurality, ranking
A = B > C would give half a point to A and B (so that the sum is 1),
and none to C, whereas ranking A > B > C would give a full point to
A and none to B or C.
Elimination would work the same way however equal rank would be
treated. If you vote A = B > C and A is eliminated, then for the
next round, your vote is B > C.
Assuming the voting machines can handle the input, where would the
expense lie in adding this support? It seems to be more a question
of whether the resulting system would be "IRV" or not... unless the
expense would be in "handling the input", but if you have a machine
that can handle A > B > C > D > E .. > Z, upgrading it to handle A =
B = C > D > E ... doesn't seem to be that expensive a change.

Huh? Noticing whether equal ranks exist; including fractions in doing
sums; etc.

Note that for the current discussion Condorcet is simpler - for each
pair of candidates count A>B or B>A if they exist.

Post by Kristofer Munsterhjelm

Post by Kristofer Munsterhjelm
From what I've seen of voting equipment, most limitations seem to
be in the name of expediency. For instance, SF's RCV three-rank
method keeps voters from ranking more than three candidates -
probably to accomodate existing equipment.

Some ways of providing for more ranks significantly burden
equipment design.
Providing for 2 ranks is essential to deserve claim as to ranks
existing; 3 helps some; more than 3 helps real voters little.

One may then ask, how many ranks are required to break Duverger's
Law? Unfortunately, I don't know the answer.

Post by Kristofer Munsterhjelm
What limitations may exist (such as your IRV example) may be
handled by having a voting machine that permits all ranking types
(full, truncated, equal rank), then having parameters that limit
according to what kind of voting system is being used in the back
end (e.g no equal rank).

Sounds like building in expensive complications.
Doing the specialization in software could be affordable.

There's a tradeoff at this point. Having a generalized machine lets
you build many that are all the same, so that you gain benefits of
scale. However, the generalized machine is more expensive because
you can't cut away what you don't need.

Post by Kristofer Munsterhjelm
It is in theory possible to make it summable - see above. The
method they did use seems not to be, though - as far as I could
see, they checked, for all possible virtual runoffs (set by
enforcing A and B as winners in the first round), whether A or B
won. Such a binary check is summable only if the results are the
same in both districts - but when they're different, one runs into
District 1 X>Y: 1000, Y>X: 990 X beats Y
District 2 X>Y: 1, Y>X: 2 Y beats X
-------------------------------------------------
Summed result X beats Y
but also
District 1 X>Y: 1000, Y>X: 990 X beats Y
District 2 X>Y: 1000, Y>X: 2000 Y beats X
-------------------------------------------------
Summed result Y beats X
In both instances, X beats Y in the first district, and Y beats X
in the second district, but the summed result is different for the
two cases. Thus I think that they would have to store the entire
Condorcet matrix (numbers of voters, not just who won) in order to
be summable. If they did, then they're summable, but if they
didn't, they aren't.

Condorcet cares not as to number of voters - for it simply sum the
matrices.

If nobody equal-ranks, then (A beats B) + (B beats A) = number of
voters. Apart from that, you're right, Condorcet doesn't care. What
I showed was that if they (the IRV proponents) tried to use only
binary arrays instead of integer arrays for their kinda-Condorcet
matrices, they would fail, because there's not enough information
there. A Condorcet matrix has to be integer (or even more fine
grained, e.g for CWP), even when that matrix is only to be used for
determining the winner of the contingent vote.

What do you do when some voters vote for neither A nor B?

Not clear to me what a binary array would be.

Post by Kristofer Munsterhjelm

Post by Kristofer Munsterhjelm
I mean freedom as a data format. A rated vote data format can
emulate a ranked vote format, as well as an approval-style data
format.

Saying freedom reminds me of something we sometimes ignore - how
much complication do we burden voters with.

Voting is already irrational from a utilitarian point of view - your
chance of affecting the outcome is way too small for it to be worth
bothering to vote, let alone consider the issues to make an informed
decision. Yet we vote anyway.
That muddies the waters, because we can't use standard utilitarian/
economic theory to find out how much complication is too much.
Perhaps people wouldn't bother with anything more than Approval, but
that seems wrong (since people rate and rank things all the time).
So, how much is too much? I don't know.

Imposing ratings for score is a noticeable complication.

Condorcet can claim a bit of simplification:
Voting as in Plurality should be encouraged whenever that meets
a voter's desires - in many races many voters need nothing more.
Voting as in Approval - ditto.
More complex ranking is really a simplification for those voters
who desire to use that ability, rather than being forced to live with
what Plurality offers.

Post by Kristofer Munsterhjelm
Of course, the user interface should be good, but that's a separate
issue. I don't particularly like general purpose direct electronic
machines, so the "user interface" may be entirely transparent - put
the appropriate number in the box next to the candidate (for each
candidate), then at some later time, OCR reads off the numbers to
parse the ballot.

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[Kristofer Munsterhjelm]

Post by Kristofer Munsterhjelm
Agreed (in turn) that forwarding ballot images doesn't make a method
summable, since otherwise, any method that doesn't care about the
order of the ballots would be "summable".
Also, IRV, in the general case, is not summable. However, what we're
talking about is the contingent vote, an "instant top-two runoff",
which is what the IRV proponents figured out how to make precinct
summable (or thought they had figured out how to make precinct
summable). It agrees with IRV if the number of candidates <= 3.
The contingent vote first counts plurality votes for the various
candidates, as top-two runoff does. Then, again as in top-two runoff,
the two "winners", Plurality wise, go to the next round. The
difference is that the contingent vote uses the same rank ballots for
the second round as for the first, only with all non-winners
eliminated, whereas true TTR has a separate second round.

Plurality and Condorcet look at the ballots ONE time, and never go
back. Does summable require this - never going back to the ballots, or
to the voters, more times?
TTR needs to go back only if the top two were near to a tie - IRV
could do the same.
For TTR the second round presumably always finishes it; get near
enough to a tie and IRV could need more rounds - but they do not mean
extra effort from the voters.

To be clear here, we're dealing with two sorts of election methods.
There are one-round methods, like Plurality, Condorcet, contingent vote,
etc.; and then there are two-or-more methods, like TTR, exhaustive
ballot, eliminate-one runoff, etc.

It's possible to turn a multiple-round method into a single-round method
by assuming the voters would never change their ballots. Doing so with
eliminate-one runoff produces IRV, and doing so with TTR produces the
Contingent Vote.

Summability is only properly defined for one-round methods. A method is
summable if it's possible to process any group of ballots into a certain
data chunk, where running the method on this data chunk produces the
same result as if it was run on that subset itself, and where two chunks
can be combined so that the same is true, and that a chunk is of size
determined by a function that increases no faster than some polynomial
of the number of candidates in the election.
Less formally, the method is summable if you can "count in precincts" to
produce managable data chunks that can then be combined to get the
result for all precincts or districts involved, no matter the size of
each district.

Post by Kristofer Munsterhjelm
Let's have a concrete example of how the contingent vote works, and
why my approach to it is summable.

[SNIP]

Post by Kristofer Munsterhjelm
There you go, the contingent vote is summable.

Not clear why the two districts were even mentioned.

The two districts were mentioned so as to show that using only the
plurality counts and Condorcet matrices for each district, one could get
the same result as by counting all the ballots combined. That is, that
the Contingent Vote (the method) is summable.

Since Condorcet was mentioned, might make sense to include a cycle and
see how much this complicates life.

Although my "summable CV" uses a Condorcet matrix, it's not a Condorcet
method. It passes Condorcet loser (like IRV), which is simple to see:
assume that the method eliminates all but the Condorcet loser and some
other candidate in the first round. Then the Condorcet loser will lose
the second round. Thus, the Condorcet loser can't win.
However, it is not Condorcet. A simple example shows this:

11: A1 > B > A2 > C
10: A2 > B > A1 > C
9: B > C > A1 > A2
8: C > B > A2 > A1

A1 and A2 go to the second round, but B is the CW.

As I say above, what qualifies as summable?

It's summable if you can merge managable-size data chunks into larger
data chunks and find the result by referring to the data chunk alone, so
that you don't have to forward the (potentially unmanagably large)
ballot data to a central location.

("Managable size" being polynomial wrt the number of candidates)

Post by Kristofer Munsterhjelm
If nobody equal-ranks, then (A beats B) + (B beats A) = number of
voters. Apart from that, you're right, Condorcet doesn't care. What I
showed was that if they (the IRV proponents) tried to use only binary
arrays instead of integer arrays for their kinda-Condorcet matrices,
they would fail, because there's not enough information there. A
Condorcet matrix has to be integer (or even more fine grained, e.g for
CWP), even when that matrix is only to be used for determining the
winner of the contingent vote.

What do you do when some voters vote for neither A nor B?

That implies either explicit equal-ranking, or truncation, which in some
sense is equal ranking last.

Not clear to me what a binary array would be.

Take a Condorcet matrix like this:

A B C beats
A --- 98 125
B 127 --- 27
C 100 198 ---

"A beats B" is true for the binary matrix iff more people voted A > B
than B > A, so

A B C beats
A - F T
B T - F
C F T -

It's not really important, though; especially not given that Kathy has
said the IRV proponents weren't doing Contingent Vote or using binary
Condorcet matrices after all.

Post by Kristofer Munsterhjelm

Post by Kristofer Munsterhjelm
I mean freedom as a data format. A rated vote data format can
emulate a ranked vote format, as well as an approval-style data format.

Saying freedom reminds me of something we sometimes ignore - how much
complication do we burden voters with.

Voting is already irrational from a utilitarian point of view - your
chance of affecting the outcome is way too small for it to be worth
bothering to vote, let alone consider the issues to make an informed
decision. Yet we vote anyway.
That muddies the waters, because we can't use standard
utilitarian/economic theory to find out how much complication is too
much. Perhaps people wouldn't bother with anything more than Approval,
but that seems wrong (since people rate and rank things all the time).
So, how much is too much? I don't know.

Imposing ratings for score is a noticeable complication.
Voting as in Plurality should be encouraged whenever that meets a
voter's desires - in many races many voters need nothing more.
Voting as in Approval - ditto.
More complex ranking is really a simplification for those voters
who desire to use that ability, rather than being forced to live with
what Plurality offers.

I think this implies that any ranked vote system should deal with less
fine-grained ballots. That is: voters should be able to bullet-vote or
vote Approval style. That, in turn, means that the ballot system should
both support explicit equal ranking (for Approval style) as well as
truncation (for Plurality type counts). Supporting truncation makes
sense in any case, because otherwise you get Australian conditions (that
degrade into a form of external party list PR through how-to-vote cards).
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[Dave Ketchum]

Post by Kristofer Munsterhjelm

Post by Dave Ketchum

Post by Kristofer Munsterhjelm
Agreed (in turn) that forwarding ballot images doesn't make a
method summable, since otherwise, any method that doesn't care
about the order of the ballots would be "summable".
Also, IRV, in the general case, is not summable. However, what
we're talking about is the contingent vote, an "instant top-two
runoff", which is what the IRV proponents figured out how to make
precinct summable (or thought they had figured out how to make
precinct summable). It agrees with IRV if the number of candidates
<= 3.
The contingent vote first counts plurality votes for the various
candidates, as top-two runoff does. Then, again as in top-two
runoff, the two "winners", Plurality wise, go to the next round.
The difference is that the contingent vote uses the same rank
ballots for the second round as for the first, only with all non-
winners eliminated, whereas true TTR has a separate second round.

Plurality and Condorcet look at the ballots ONE time, and
never go back. Does summable require this - never going back to
the ballots, or to the voters, more times?
TTR needs to go back only if the top two were near to a tie -
IRV could do the same.
For TTR the second round presumably always finishes it; get
near enough to a tie and IRV could need more rounds - but they do
not mean extra effort from the voters.

To be clear here, we're dealing with two sorts of election methods.
There are one-round methods, like Plurality, Condorcet, contingent
vote, etc.; and then there are two-or-more methods, like TTR,
exhaustive ballot, eliminate-one runoff, etc.
It's possible to turn a multiple-round method into a single-round
method by assuming the voters would never change their ballots.
Doing so with eliminate-one runoff produces IRV, and doing so with
TTR produces the Contingent Vote.

Let's try it slowly for IRV, assuming multiple districts to avoid
shortcut temptations:

1 Count ala Plurality. If leader has a majority, that is winner.

2 Sum vote counts, starting with weakest count and ending before doing
the next candidate that would make a majority. None of those counted
could win, so mark them all as losers and go back to step 1.

Never needing step 2 is single round. In IRV voters do not have
opportunity to change ballots - but step 2 to decide on losers and
recounts is not avoidable. Note that with three candidates step 2 is
trivial for there is only one candidate for it to find.
But, with four candidates, such as A 29 , B 28, C 27 , D 5, only
D can be discarded for round 2 - but for A 29 , B 28, C 6 , D 5, C and
D can be discarded for second (final) round.

Post by Kristofer Munsterhjelm
Summability is only properly defined for one-round methods. A method
is summable if it's possible to process any group of ballots into a
certain data chunk, where running the method on this data chunk
produces the same result as if it was run on that subset itself, and
where two chunks can be combined so that the same is true, and that
a chunk is of size determined by a function that increases no faster
than some polynomial of the number of candidates in the election.
Less formally, the method is summable if you can "count in
precincts" to produce managable data chunks that can then be
combined to get the result for all precincts or districts involved,
no matter the size of each district.

Not clear how this helps. You have to get the totals for round 1 to
decide how to proceed - matters not how many chunks.

Post by Kristofer Munsterhjelm

Post by Dave Ketchum

Post by Kristofer Munsterhjelm
Let's have a concrete example of how the contingent vote works,
and why my approach to it is summable.

[SNIP]

Post by Dave Ketchum

Post by Kristofer Munsterhjelm
There you go, the contingent vote is summable.

Not clear why the two districts were even mentioned.

The two districts were mentioned so as to show that using only the
plurality counts and Condorcet matrices for each district, one could
get the same result as by counting all the ballots combined. That
is, that the Contingent Vote (the method) is summable.

Huh!

Post by Kristofer Munsterhjelm

Post by Dave Ketchum
Since Condorcet was mentioned, might make sense to include a cycle
and see how much this complicates life.

Although my "summable CV" uses a Condorcet matrix, it's not a
Condorcet method. It passes Condorcet loser (like IRV), which is
simple to see: assume that the method eliminates all but the
Condorcet loser and some other candidate in the first round. Then
the Condorcet loser will lose the second round. Thus, the Condorcet
loser can't win.
11: A1 > B > A2 > C
10: A2 > B > A1 > C
9: B > C > A1 > A2
8: C > B > A2 > A1
A1 and A2 go to the second round, but B is the CW.

Post by Dave Ketchum
As I say above, what qualifies as summable?

It's summable if you can merge managable-size data chunks into
larger data chunks and find the result by referring to the data
chunk alone, so that you don't have to forward the (potentially
unmanagably large) ballot data to a central location.
("Managable size" being polynomial wrt the number of candidates)

Post by Dave Ketchum

Post by Kristofer Munsterhjelm
If nobody equal-ranks, then (A beats B) + (B beats A) = number of
voters. Apart from that, you're right, Condorcet doesn't care.
What I showed was that if they (the IRV proponents) tried to use
only binary arrays instead of integer arrays for their kinda-
Condorcet matrices, they would fail, because there's not enough
information there. A Condorcet matrix has to be integer (or even
more fine grained, e.g for CWP), even when that matrix is only to
be used for determining the winner of the contingent vote.

What do you do when some voters vote for neither A nor B?

That implies either explicit equal-ranking, or truncation, which in
some sense is equal ranking last.

We have IRV ballots permitting only 3 ranks - with more than three
candidates.

Post by Kristofer Munsterhjelm

Post by Dave Ketchum
Not clear to me what a binary array would be.

Clearly not useful here.

Post by Kristofer Munsterhjelm
A B C beats
A --- 98 125
B 127 --- 27
C 100 198 ---
"A beats B" is true for the binary matrix iff more people voted A >
B than B > A, so
A B C beats
A - F T
B T - F
C F T -
It's not really important, though; especially not given that Kathy
has said the IRV proponents weren't doing Contingent Vote or using
binary Condorcet matrices after all.

Post by Dave Ketchum

Post by Kristofer Munsterhjelm

Post by Kristofer Munsterhjelm
I mean freedom as a data format. A rated vote data format can
emulate a ranked vote format, as well as an approval-style data format.

Saying freedom reminds me of something we sometimes ignore - how
much complication do we burden voters with.

Voting is already irrational from a utilitarian point of view -
your chance of affecting the outcome is way too small for it to be
worth bothering to vote, let alone consider the issues to make an
informed decision. Yet we vote anyway.
That muddies the waters, because we can't use standard utilitarian/
economic theory to find out how much complication is too much.
Perhaps people wouldn't bother with anything more than Approval,
but that seems wrong (since people rate and rank things all the
time). So, how much is too much? I don't know.

Imposing ratings for score is a noticeable complication.
Voting as in Plurality should be encouraged whenever that meets
a voter's desires - in many races many voters need nothing more.
Voting as in Approval - ditto.
More complex ranking is really a simplification for those
voters who desire to use that ability, rather than being forced to
live with what Plurality offers.

I think this implies that any ranked vote system should deal with
less fine-grained ballots. That is: voters should be able to bullet-
vote or vote Approval style. That, in turn, means that the ballot
system should both support explicit equal ranking (for Approval
style) as well as truncation (for Plurality type counts). Supporting
truncation makes sense in any case, because otherwise you get
Australian conditions (that degrade into a form of external party
list PR through how-to-vote cards).

Your use of "truncation" bothers - I think of it as the system
discarding what it sees as excess data rather than the voter choosing
to say less than the method's limits.



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[Kristofer Munsterhjelm]

Post by Dave Ketchum

Post by Kristofer Munsterhjelm
To be clear here, we're dealing with two sorts of election methods.
There are one-round methods, like Plurality, Condorcet, contingent
vote, etc.; and then there are two-or-more methods, like TTR,
exhaustive ballot, eliminate-one runoff, etc.
It's possible to turn a multiple-round method into a single-round
method by assuming the voters would never change their ballots. Doing
so with eliminate-one runoff produces IRV, and doing so with TTR
produces the Contingent Vote.

Let's try it slowly for IRV, assuming multiple districts to avoid
1 Count ala Plurality. If leader has a majority, that is winner.
2 Sum vote counts, starting with weakest count and ending before doing
the next candidate that would make a majority. None of those counted
could win, so mark them all as losers and go back to step 1.
Never needing step 2 is single round. In IRV voters do not have
opportunity to change ballots - but step 2 to decide on losers and
recounts is not avoidable. Note that with three candidates step 2 is
trivial for there is only one candidate for it to find.
But, with four candidates, such as A 29 , B 28, C 27 , D 5, only D
can be discarded for round 2 - but for A 29 , B 28, C 6 , D 5, C and D
can be discarded for second (final) round.

I'm not talking about IRV. I'm talking about the Contingent Vote. IRV is
to exhaustive runoff (do balloting, remove loser, do another balloting,
remove loser, ...) as CV is to top two runoff.

I'm talking about the Contingent Vote because that was what I thought
they were emulating. CV is not a particularly good voting method, in itself.

Again, the steps for the Contingent vote is as follows:
1 - Do a plurality count. If someone has a majority, he wins.
2 - Otherwise, eliminate all but the top two. Reread the ballots with
all but the top two eliminated. Whoever has the greatest Plurality count
(i.e, is voted above the other more often) wins.

Do you see that the first step can be done by a plurality count, which
is summable, to find the top two? Also, do you see that the second can
be checked by a pairwise comparison, no matter who the top two are?
(Although, of course, it's a different pairwise comparison depending on
who the top two are)

Post by Dave Ketchum

Post by Kristofer Munsterhjelm
Summability is only properly defined for one-round methods. A method
is summable if it's possible to process any group of ballots into a
certain data chunk, where running the method on this data chunk
produces the same result as if it was run on that subset itself, and
where two chunks can be combined so that the same is true, and that a
chunk is of size determined by a function that increases no faster
than some polynomial of the number of candidates in the election.
Less formally, the method is summable if you can "count in precincts"
to produce managable data chunks that can then be combined to get the
result for all precincts or districts involved, no matter the size of
each district.

Not clear how this helps. You have to get the totals for round 1 to
decide how to proceed - matters not how many chunks.

I never claimed IRV itself to be summable, just that the Contingent Vote
is. I don't think it's possible to make IRV (the proper method) summable
at all - the chaotic aspect that makes it nonmonotonic and causes those
weird shapes in the Yee diagrams hints at that (small change in votes -
large change in outcome).

Post by Dave Ketchum

Post by Kristofer Munsterhjelm
The two districts were mentioned so as to show that using only the
plurality counts and Condorcet matrices for each district, one could
get the same result as by counting all the ballots combined. That is,
that the Contingent Vote (the method) is summable.

Huh!

I claimed it was summable. Then I showed it for a particular instance by
first showing the result by counting both districts as one (central
count), then showing the "data chunk" for each district, summing them,
and showing that the result using the summed chunks was the same as the
result by central count.

Post by Dave Ketchum

Post by Kristofer Munsterhjelm

Post by Dave Ketchum

Post by Kristofer Munsterhjelm
If nobody equal-ranks, then (A beats B) + (B beats A) = number of
voters. Apart from that, you're right, Condorcet doesn't care. What
I showed was that if they (the IRV proponents) tried to use only
binary arrays instead of integer arrays for their kinda-Condorcet
matrices, they would fail, because there's not enough information
there. A Condorcet matrix has to be integer (or even more fine
grained, e.g for CWP), even when that matrix is only to be used for
determining the winner of the contingent vote.

What do you do when some voters vote for neither A nor B?

That implies either explicit equal-ranking, or truncation, which in
some sense is equal ranking last.

We have IRV ballots permitting only 3 ranks - with more than three
candidates.

Ah, yes. SF's RCV is sort of summable, though. Because there are only
three ranks, the possible number of unique ballots are:

n * (n-1) * (n-2)

where n is the number of candidates. This increases more slowly than
n^3, hence the data chunk (which simply consists of the ballots
themselves, each prefixed by how many voted this way), is polynomial
with regards to the number of candidates.

With explicit equal rank, the equation is somewhat more complex. If by
"3 ranks", A = B = C count as 3 ranks, then it's still summable. If A =
B = C only counts as a single rank, then it's not.

Post by Dave Ketchum

Post by Kristofer Munsterhjelm
I think this implies that any ranked vote system should deal with less
fine-grained ballots. That is: voters should be able to bullet-vote or
vote Approval style. That, in turn, means that the ballot system
should both support explicit equal ranking (for Approval style) as
well as truncation (for Plurality type counts). Supporting truncation
makes sense in any case, because otherwise you get Australian
conditions (that degrade into a form of external party list PR through
how-to-vote cards).

Your use of "truncation" bothers - I think of it as the system
discarding what it sees as excess data rather than the voter choosing to
say less than the method's limits.

Truncation is a term that's been used on EM before. It simply means
stopping the ranking before you have ranked everyone. The machine or
method doesn't truncate, the voter does.

See, for instance,
http://lists.electorama.com/pipermail/election-methods-electorama.com/2002-
September/008656.html , which is an EM post (from 2002) where the term
"truncation" is used.
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[Raph Frank]

Let's try it slowly for IRV, assuming multiple districts to avoid shortcut
1 Count ala Plurality. If leader has a majority, that is winner.
2 Sum vote counts, starting with weakest count and ending before doing the
next candidate that would make a majority. None of those counted could win,
so mark them all as losers and go back to step 1.

That isn't true.

The rule is actually that you can eliminate the weakest N candidates
in one step, if the sum of their votes is less than the (N+1)th
weakest candidates. The procedure is then to find the largest
possible N.

40: A
25: B
15: C>E>B
9: D>E>B
7: E>B
4: F>E>B

Round 1:
A: 40
B: 25
C: 15
D: 9
E: 7
F: 4

According to your rules, eliminate F+E+D+C. Eliminating B as well
would cause a majority of votes, so B is safe.

Round 2:
A: 40
B: 60

B wins

However, with full IRV, the results are

eliminat F

Round 2
A: 40
B: 25
C: 15
D: 9
E: 7+4 = 11
F: -

Eliminate D

Round 3
A: 40
B: 25
C: 15
D: -
E: 9+11 = 20
F: -

Eliminate C

Round 3
A: 40
B: 25
C: -
D: -
E: 20+15 = 35
F: -

Eliminate B

Round 4

A: 40
B: -
C: -
D: -
E: 35+25 = 60
F: -

E wins

So, the result is different.

Post by Kristofer Munsterhjelm
Less formally, the method is summable if you can "count in precincts" to
produce managable data chunks that can then be combined to get the result
for all precincts or districts involved, no matter the size of each
district.

Not clear how this helps. You have to get the totals for round 1 to decide
how to proceed - matters not how many chunks.

I guess IRV is "summable in precincts, subject to central office instructions".

An election can be verified by checking all the precinct sums/counts
and that the central instructions were correct, assuming that the
precinct sums were also correct.
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[Dave Ketchum]

Ouch - What I said about IRV missed a bit. Matters little for I still
dislike IRV or Contingent Vote (which I read as running a bit faster
and more often picking the wrong winner).

Post by Raph Frank

Let's try it slowly for IRV, assuming multiple districts to avoid shortcut
1 Count ala Plurality. If leader has a majority, that is winner.
2 Sum vote counts, starting with weakest count and ending before doing the
next candidate that would make a majority. None of those counted could win,
so mark them all as losers and go back to step 1.

That isn't true.
The rule is actually that you can eliminate the weakest N candidates
in one step, if the sum of their votes is less than the (N+1)th
weakest candidates. The procedure is then to find the largest
possible N.
40: A
25: B
15: C>E>B
9: D>E>B
7: E>B
4: F>E>B
A: 40
B: 25
C: 15
D: 9
E: 7
F: 4
According to your rules, eliminate F+E+D+C. Eliminating B as well
would cause a majority of votes, so B is safe.
A: 40
B: 60
B wins
However, with full IRV, the results are
eliminat F
Round 2
A: 40
B: 25
C: 15
D: 9
E: 7+4 = 11
F: -
Eliminate D
Round 3
A: 40
B: 25
C: 15
D: -
E: 9+11 = 20
F: -
Eliminate C
Round 3
A: 40
B: 25
C: -
D: -
E: 20+15 = 35
F: -
Eliminate B

OOPS here - The B voters did not name a next rank so 40 A beats 35 E!

DWK

Post by Raph Frank
Round 4
A: 40
B: -
C: -
D: -
E: 35+25 = 60
F: -
E wins
So, the result is different.

Post by Kristofer Munsterhjelm
Less formally, the method is summable if you can "count in
precincts" to
produce managable data chunks that can then be combined to get the result
for all precincts or districts involved, no matter the size of each
district.

Not clear how this helps. You have to get the totals for round 1 to decide
how to proceed - matters not how many chunks.

I guess IRV is "summable in precincts, subject to central office instructions".
An election can be verified by checking all the precinct sums/counts
and that the central instructions were correct, assuming that the
precinct sums were also correct.

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[Raph Frank]

Post by Dave Ketchum
OOPS here - The B voters did not name a next rank so 40 A beats 35 E!

Bah, it's kinda like if you correct someone's grammer in a post, you
are more likely to have a grammer mistake yourself :p.
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[Kathy Dopp]

Date: Mon, 23 Mar 2009 15:46:44 +0100
Subject: Re: [EM] IRV proponents figure out how to make IRV
       precinct-summable
Also, IRV, in the general case, is not summable. However, what we're talking about is the contingent vote, an "instant top-two runoff", which is what the IRV proponents figured out how to make precinct summable (or thought they had figured out how to make precinct summable).

No. It was my mistake to misnomer the Subject on my email that started
this thread.

The NC folks did not find a way to make IRV precinct-summable, they
merely found a way to count round #2 in the polling locations *after*
they'd waited there for however long it takes to count round #1 at the
central office. Of course round #1 of IRV is always precinct-summable,
but no other round ever is.

I've corrected and added to my original email post at this blog entry:
http://kathydopp.com/serendipity/index.php?/archives/41-North-Carolina-develops-method-to-count-IRV-with-precinct-opti-scanners.html

The only way to make IRV precinct-summable would be to report all the
sums for each permutation of possible ballot orderings, including
partial orderings, but that is a HUGE number of sums, usually more
sums than the total number of voters voting in any precinct whenever
there are a large number of candidates. I've given the formula for
how to calculate how many sums would have to be reported to make IRV
precinct-summable in my paper "The 18 Flaws and 4 Benefits of IRV..."
posted here:

http://electionmathematics.org/ucvAnalysis/US/RCV-IRV/InstantRunoffVotingFlaws.pdf

Sorry bout the mixup. We should change the Subject of this thread to
correct the misunderstanding I began.

Cheers,

Kathy
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[Juho Laatu]

<http://lists.electorama.com/htdig.cgi/election-methods-electorama.com/2001-September/006595.html>
Buddha Buck replied with an IRV example that much more

clearly explained

<http://lists..electorama.com/htdig.cgi/election-methods-electorama.com/2001-September/006598.html>
Quite neat I think.

Yes, but...what's the point? That is, what problem are you
trying to solve, exactly?
If you're in a position to compute the matrix, why not
simply send the file of ballot data? It's not as if it's
going to be prohibitively large. The 2008 US Presidential
election had ~13 million votes in California, the largest
state. Ten candidates at a byte per candidate would only be
order of a 100MB for the entire state, before compression.
Heck, I've got mp3's bigger than that.

Yes, good question. IRV votes thus don't
take excessive amount of space and can be
compressed and can be summed up (although
not very compactly).

Possible answers might include:

1) To help verifying the vote counting
process. If the partial results are
counted/verified already locally it may
be more difficult to falsify the results.
With the modern personal computers it is
however also possible to anyone to collect
all the <100MB files in one's own computer
and verify the election if all the
districts publish their ballots.

2) To build trust on the system by
showing the partial results to people.
In this case the summed partial results
should be very simple so that every
regular voter can see that they are ok.
A Condorcet pairwise comparison matrix
might be too difficult. Sum of votes per
each candidate could be simple enough.
Also publishing the outcome of the
election based on the votes of one
district alone can help (although these
results would not be further used /
usable when summing up the results).
This is easy enough for all methods.
And the voters will see if the results
are credible, not e.g. opposite to what
everyone expected.

3) For general interest. The local
results in point 2 above are certainly
interesting. One must be capable of
summing up the results so that one can
see what happened. Also this case does
not set a requirement of reusing these
"summed up" results later in the process
when the election wide results are
counted (raw ballot data will do).
(Also the Condorcet pairwise matrix may
be very interesting material to study
and speculate on.)

4) To hide the individual votes for
privacy and security reasons. Published
ranked votes open up some doors for vote
buying and coercion. It is quite easy to
generate unique votes when the number of
candidates increases. (Also individual
ballots are interesting from point 1, 2
and 3 point of view, but dangerous.)

5) To distribute the load of vote
counting and to speed up the process.
This mostly applies to hand counting.
In the time of computers it may be
enough to just digitize the votes
locally (unless already digital) and
to verify these transformations.

6) To keep possible recounts local. This
is also mainly related to hand counting.
Nowadays local re-digitization may often
be enough..

In summary, maybe raw digitized ballots
are good enough in most cases for the
computers, but humans may need more
compact information (not necessarily
summable) for various reasons. The
privacy point may set requirements on
what to publish and what not (some
countries are already now quite strict
on this). In IRV there may thus be a
need to keep the ballots hidden or to
break them in such a way that individual
ballots can not be recognized (or
verified to the buyer/coercer).

Juho








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[Raph Frank]

Post by Juho Laatu
4) To hide the individual votes for
privacy and security reasons. Published
ranked votes open up some doors for vote
buying and coercion. It is quite easy to
generate unique votes when the number of
candidates increases. (Also individual
ballots are interesting from point 1, 2
and 3 point of view, but dangerous.)

One option here would be to restrict the number of rankings. If the
number of voters is higher than Candidates ^ Rankings, then most
possible configurations are likely to receive at least 1 'hit'.

Another option would be to do it based on the ballot data. For example

1) Start with 1 "pile" of all the ballots
2) Split all piles into sub-piles based on highest ranked difference
3) For each group of sub-piles (from same pile), combine the smallest
sub-piles together until the smallest has at least N N (say 10)
ballots,
4) Declare all sub-piles as piles and return to 2), unless no change
was made in 3)

So, if the ballots were

30) A>B>C
20) C>A>D
13) C>B>D
1) A>B>C>X>Y>Z

The process would be:

Pass 1
Pile A>
30) A>B>C
1) A>B>C>X>Y>Z

Pile C>
20) C>A>D
13) C>B>D

Pass 2:
Pile A>B
30) A>B>C
1) A>B>C>X>Y>Z

Pile C>A
20) C>A>D

Pile C>B
13) C>B>D

Pass 3:
Pile A>B>C
30) A>B>C
1) A>B>C>X>Y>Z

Pile C>A>D
20) C>A>D

Pile C>B>D
13) C>B>D

Pass 3:
Sub-Pile A>B>C
30) A>B>C

Sub-Pile A>B>C>X
1) A>B>C>X>Y>Z

Pile C>A>D
20) C>A>D

Pile C>B>D
13) C>B>D

Sub-pile A>B>C>X hasn't enough ballots, so is combined with the next
lowest sub-pile, A>B>C

Pile A>B>C
30) A>B>C
1) A>B>C>X>Y>Z

Pile C>A>D
20) C>A>D

Pile C>B>D
13) C>B>D

No change has occured, so end.

The results would be declared as

31) A>B>C
20) C>A>D
13) C>B>D

This gives a loss of accuracy, but hopefully not to much.

Also, it doesn't work if you are providing ballot images.

Post by Juho Laatu
In summary, maybe raw digitized ballots
are good enough in most cases for the
computers, but humans may need more
compact information (not necessarily
summable) for various reasons.

The theory was that the ballots would be published and
non-profit/bored programmers could convert them into rankings.

The government would publish a block of ballots and their associated
official rankings.

If there was errors, it would be possible for them to provide a series
of links to offical ballot/rankings pairs which clearly don't match
what is actually on the image.

Post by Juho Laatu
The
privacy point may set requirements on
what to publish and what not (some
countries are already now quite strict
on this).

You could have a rule that a ballot is only valid if it doesn't have
marks. Also, ballots images could have parts of the image censored,
to cover up those marks. Ofc, the actual boxes where the person
indicates the rankings would have to be shown.

This somewhat goes against the principle of multiple independent
groups imaging the ballots for comparison to the official list. In
principle, you could require that they mask off all parts of the image
other than the ranking boxes and the ballot ID number.

I guess it depends on the lengths people would go to. In principle,
you could require that the seller use a special font when filling in
their ballot.
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[Jonathan Lundell]

Post by Juho Laatu
Yes, good question. IRV votes thus don't
take excessive amount of space and can be
compressed and can be summed up (although
not very compactly).
1) To help verifying the vote counting
process. If the partial results are
counted/verified already locally it may
be more difficult to falsify the results.
With the modern personal computers it is
however also possible to anyone to collect
all the <100MB files in one's own computer
and verify the election if all the
districts publish their ballots.

It does seem that this kind of universal verification could be useful
for any system in which counting is nontrivial. WRT IRV, one could at
least publish the results of a local IRV count--the counts for each
candidate at each round. Whether that's useful for verifying the
process isn't all that clear to me, but it would carry a fair amount
of information, and could be verified against a similar count at the
central counting facility.

Post by Juho Laatu
2) To build trust on the system by
showing the partial results to people.
In this case the summed partial results
should be very simple so that every
regular voter can see that they are ok.
A Condorcet pairwise comparison matrix
might be too difficult. Sum of votes per
each candidate could be simple enough.
Also publishing the outcome of the
election based on the votes of one
district alone can help (although these
results would not be further used /
usable when summing up the results).
This is easy enough for all methods.
And the voters will see if the results
are credible, not e.g. opposite to what
everyone expected.

As you say, easy enough for all methods.

Post by Juho Laatu
3) For general interest. The local
results in point 2 above are certainly
interesting. One must be capable of
summing up the results so that one can
see what happened. Also this case does
not set a requirement of reusing these
"summed up" results later in the process
when the election wide results are
counted (raw ballot data will do).
(Also the Condorcet pairwise matrix may
be very interesting material to study
and speculate on.)

Or even a tabulation (for ranked systems) of the count at each rank.

Post by Juho Laatu
4) To hide the individual votes for
privacy and security reasons. Published
ranked votes open up some doors for vote
buying and coercion. It is quite easy to
generate unique votes when the number of
candidates increases. (Also individual
ballots are interesting from point 1, 2
and 3 point of view, but dangerous.)

This is a difficult tough problem for many "open voting" proposals.
Ballot publication is a powerful tool for verification, but
potentially violates secret-ballot principles.

A compromise approach for IRV ballots (though not, I think, Condorcet)
would be to publish a summary of first place choices, determine the
"hopeless" candidates (those that can safely be eliminated in the
first round), and then purge the ballot file of those candidates
before publishing the file. At least in a relatively large election, I
think this would be an adequate measure to deal with the
"fingerprinting" problem.

Post by Juho Laatu
5) To distribute the load of vote
counting and to speed up the process.
This mostly applies to hand counting.
In the time of computers it may be
enough to just digitize the votes
locally (unless already digital) and
to verify these transformations.
6) To keep possible recounts local. This
is also mainly related to hand counting.
Nowadays local re-digitization may often
be enough..

Or perhaps hand-verification of the digitization.

Post by Juho Laatu
In summary, maybe raw digitized ballots
are good enough in most cases for the
computers, but humans may need more
compact information (not necessarily
summable) for various reasons. The
privacy point may set requirements on
what to publish and what not (some
countries are already now quite strict
on this). In IRV there may thus be a
need to keep the ballots hidden or to
break them in such a way that individual
ballots can not be recognized (or
verified to the buyer/coercer).

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[Juho Laatu]

On Wed, Mar 25, 2009 at 7:19 AM, Juho

Post by Juho Laatu
4) To hide the individual votes for
privacy and security reasons. Published
ranked votes open up some doors for vote
buying and coercion. It is quite easy to
generate unique votes when the number of
candidates increases. (Also individual
ballots are interesting from point 1, 2
and 3 point of view, but dangerous.)

One option here would be to restrict the number of
rankings.  If the
number of voters is higher than Candidates ^ Rankings, then
most
possible configurations are likely to receive at least 1
'hit'.

Yes, that would be one approach.
One should be however careful
since although slight limitations
could have no meaningful impact
too short ballots could lead to
significant number of ballots
that didn't cover the important
preferences.

Note also that vote buying and
coercion may also tolerate
reduced probabilities. For
example a coerced voter may not
dare to vote otherwise than as
told even if there was only a
10% chance of getting caught of
voting otherwise.

With some rules one can also
generate some unusual votes. For
example in the recent Burlington
mayoral IRV election votes like
A>B>C>D=F were valid. they were
considered exhausted only if
both D and F are still in the
race when the counting reaches
those preferences in this ballot
(D or F may be a minor candidate
that certainly will be eliminated
early). this thus makes it
possible to generate unique
ballots even when all the regular
voting patterns are too common to
be used for buying/coercion.

Another option would be to do it based on the ballot
data.  For example
1) Start with 1 "pile" of all the ballots
2) Split all piles into sub-piles based on highest ranked
difference
3) For each group of sub-piles (from same pile), combine
the smallest
sub-piles together until the smallest has at least N N (say
10)
ballots,
4) Declare all sub-piles as piles and return to 2), unless
no change
was made in 3)
So, if the ballots were
30) A>B>C
20) C>A>D
13) C>B>D
1) A>B>C>X>Y>Z
Pass 1
Pile A>
30) A>B>C
1) A>B>C>X>Y>Z
Pile C>
20) C>A>D
13) C>B>D
Pile A>B
30) A>B>C
1) A>B>C>X>Y>Z
Pile C>A
20) C>A>D
Pile C>B
13) C>B>D
Pile A>B>C
30) A>B>C
1) A>B>C>X>Y>Z
Pile C>A>D
20) C>A>D
Pile C>B>D
13) C>B>D
Sub-Pile A>B>C
30) A>B>C
Sub-Pile A>B>C>X
1) A>B>C>X>Y>Z
Pile C>A>D
20) C>A>D
Pile C>B>D
13) C>B>D
Sub-pile A>B>C>X hasn't enough ballots, so is
combined with the next
lowest sub-pile, A>B>C
Pile A>B>C
30) A>B>C
1) A>B>C>X>Y>Z
Pile C>A>D
20) C>A>D
Pile C>B>D
13) C>B>D
No change has occured, so end.
The results would be declared as
31) A>B>C
20) C>A>D
13) C>B>D
This gives a loss of accuracy, but hopefully not to much.
Also, it doesn't work if you are providing ballot images.

Yes, ballot images and
requirement of secret
votes is a bad mix.

Post by Juho Laatu
In summary, maybe raw digitized ballots
are good enough in most cases for the
computers, but humans may need more
compact information (not necessarily
summable) for various reasons.

The theory was that the ballots would be published and
non-profit/bored programmers could convert them into
rankings.
The government would publish a block of ballots and their
associated
official rankings.
If there was errors, it would be possible for them to
provide a series
of links to offical ballot/rankings pairs which clearly
don't match
what is actually on the image.

Post by Juho Laatu
The
privacy point may set requirements on
what to publish and what not (some
countries are already now quite strict
on this).

You could have a rule that a ballot is only valid if it
doesn't have
marks.

This must be a common practice
in many places.

Juho

  Also, ballots images could have parts of the
image censored,
to cover up those marks.  Ofc, the actual boxes where
the person
indicates the rankings would have to be shown.
This somewhat goes against the principle of multiple
independent
groups imaging the ballots for comparison to the official
list.  In
principle, you could require that they mask off all parts
of the image
other than the ranking boxes and the ballot ID number.
I guess it depends on the lengths people would go to. 
In principle,
you could require that the seller use a special font when
filling in
their ballot.

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[Juho Laatu]

On Mar 25, 2009, at 12:19 AM, Juho

Post by Juho Laatu
Yes, good question. IRV votes thus don't
take excessive amount of space and can be
compressed and can be summed up (although
not very compactly).
1) To help verifying the vote counting
process. If the partial results are
counted/verified already locally it may
be more difficult to falsify the results.
With the modern personal computers it is
however also possible to anyone to collect
all the <100MB files in one's own computer
and verify the election if all the
districts publish their ballots.

It does seem that this kind of universal verification could
be useful for any system in which counting is nontrivial.
WRT IRV, one could at least publish the results of a local
IRV count--the counts for each candidate at each round.
Whether that's useful for verifying the process isn't all
that clear to me, but it would carry a fair amount of
information, and could be verified against a similar count
at the central counting facility.

Yes, this already builds some
trust among the local people
when they see that the votes
are about what they wold expect
them to be. Local officials
(=representative of all interest
groups) with access to the local
ballots could also monitor the
election wide process locally
at the same time (even if the
official counting process
would be centralized).

In general I do think that much
can be achieved already with
well organized local vote
digitization (and summing)
process where all interest
groups are present. I think
this (and well working reliable
ballot format) is a much better
approach than possible recounts
and other debates after the
event. One can add the above
mentioned monitoring of
centralized counting process
(that may be needed if the
ballots are not properly
summable) to this.

Post by Juho Laatu
2) To build trust on the system by
showing the partial results to people.
In this case the summed partial results
should be very simple so that every
regular voter can see that they are ok.
A Condorcet pairwise comparison matrix
might be too difficult. Sum of votes per
each candidate could be simple enough.
Also publishing the outcome of the
election based on the votes of one
district alone can help (although these
results would not be further used /
usable when summing up the results).
This is easy enough for all methods.
And the voters will see if the results
are credible, not e.g. opposite to what
everyone expected.

As you say, easy enough for all methods.

Post by Juho Laatu
3) For general interest. The local
results in point 2 above are certainly
interesting. One must be capable of
summing up the results so that one can
see what happened. Also this case does
not set a requirement of reusing these
"summed up" results later in the process
when the election wide results are
counted (raw ballot data will do).
(Also the Condorcet pairwise matrix may
be very interesting material to study
and speculate on.)

Or even a tabulation (for ranked systems) of the count at
each rank.

Post by Juho Laatu
4) To hide the individual votes for
privacy and security reasons. Published
ranked votes open up some doors for vote
buying and coercion. It is quite easy to
generate unique votes when the number of
candidates increases. (Also individual
ballots are interesting from point 1, 2
and 3 point of view, but dangerous.)

This is a difficult tough problem for many "open voting"
proposals. Ballot publication is a powerful tool for
verification, but potentially violates secret-ballot
principles.

Yes. I already noted the
importance of good local
procedures when digitizing the
votes. That is one key approach
to fighting this problem (and
gaining trust by other means
than public ballots or ballot
images).

A compromise approach for IRV ballots (though not, I think,
Condorcet) would be to publish a summary of first place
choices, determine the "hopeless" candidates (those that can
safely be eliminated in the first round), and then purge the
ballot file of those candidates before publishing the file.
At least in a relatively large election, I think this would
be an adequate measure to deal with the "fingerprinting"
problem.

Yes but one may need to do first
a centralized analysis on which
candidates are weak enough
before daring to drop them out.

Post by Juho Laatu
5) To distribute the load of vote
counting and to speed up the process.
This mostly applies to hand counting.
In the time of computers it may be
enough to just digitize the votes
locally (unless already digital) and
to verify these transformations.
6) To keep possible recounts local. This
is also mainly related to hand counting.
Nowadays local re-digitization may often
be enough..

Or perhaps hand-verification of the digitization.

Yes, maybe part of 5.

Juho

Post by Juho Laatu
In summary, maybe raw digitized ballots
are good enough in most cases for the
computers, but humans may need more
compact information (not necessarily
summable) for various reasons. The
privacy point may set requirements on
what to publish and what not (some
countries are already now quite strict
on this). In IRV there may thus be a
need to keep the ballots hidden or to
break them in such a way that individual
ballots can not be recognized (or
verified to the buyer/coercer).

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