Post by Juho LaatuPost by Kristofer MunsterhjelmAlright. You may like Minmax for being Minmax, and
that's okay; but in my case, I'm not sure if it
would withstand strategy (there's that "hard to
estimate the amount of strategy that will happen"
again), and the Minmax heuristic itself doesn't seem
important enough to trade things like clone independence and
Smith for.
The good points in Minmax are related to behaviour
with sincere votes. It is not really rigged to
remove maximum number or amount of strategic threats
(but to implement one natural sincere utility
function). The question then is which properties one
should emphasize (electing the right winner vs. not
electing a wrong winner due to strategic voting).
All Condoret methods are vulnerable to some very
basic strategies. Some Condorcet methods try to
fix some additional threats. One may say that
differences in the level of vulnerability are not
that big. And fixing one problem often leads to
vulnerability on some other area.
There is probably a Pareto front in this respect. Just like some methods
fail more criteria than others, some methods would do both worse on
sincere votes and resist strategy less; it would be Pareto-dominated by
better methods. But since there's a Pareto front and not a single
objective, some methods on that front will be better at translating
sincere expression (whatever metric is used to measure this), while some
are much more resistant against strategy.
If we take that further, some compliances are probably more "expensive"
than others. Intuitively, I think clone independence is pretty
inexpensive (that it alters situations that is much more likely to be
due to strategy than honest voting), but I have no proof of this, of
course; and similarly intuitively, I think that MDQBR (mutual dominant
quarter burial resistance) would be very expensive, since so many voters
are burying that the dishonest ballot bundle will collide with a sincere
ballot bundle (in the latter case, the "buriers' candidate" should win,
because there are no buriers and the expression is sincere).
Post by Juho LaatuOne may say that all Condorcet methods are quite
resistant to strategic voting, espacially in the
typical environments (large public elections with
independent decision making and with limited
information on how others are going to vote).
That's what it all boils down to. We don't know whether Condorcet
methods are adequately resistant. The cover-all-bases approach is to try
to have the method pass as many criteria as possible so that even in the
worst case, the system resists strategy. If the criteria are cheap,
there's little harm (except the waste of work, but having a margin of
safety is probably a good thing, ceteris paribus). The other approach
would be to actually investigate the kind of strategy that would
develop, but this is difficult: even if we had access to near-unlimited
numbers of experiments, we wouldn't know whether the dynamics would lead
to things like vote management on one hand, or the initial strategy
resistance would discourage people from building upon them on the other.
Post by Juho LaatuI say this to present Minmax in a positive light.
Maybe the fairness of the method is also a
positive value. Maybe the strategic defences are
not needed, especially since there is a risk that
we don't elect the best winner then. Maybe focus
on the positive properties even encourages sincere
voting (=let's just pick the best winner). Maybe
the Minmax viewpoint to who is best is accurate
enough for the purpose.
And if there are meninful strategies and counter
strategies then I think the method may already
have failed.
Minmax is not necessarily the ideal utility
function (for ranked votes). I think different
elections may well have different sincere needs.
Different methods may be used for different needs.
In Minmax it is quite easy to justify electing
Condorcet loser (in some very rare cases) or to
fail strict clone compliancy (in some very rare
cases). Also mutual majority can be explained away
(I already tried this in this mail stream) but
here it is easier to give space also to other
opinions.
This raises the question: for ranked electoral methods, what is the
ideal utility function, or more precisely, what is the ideal honest
aggregation function? One may argue for Borda being it (Bayesian
regret), or Minmax (gives up as little as possible), Kemeny-Young
(maximum likelihood, maximize the number of voters that agree with each
preference) or Dodgson (minimize ballot differences to CW). In the case
of different ideal functions for different needs, the question is
displaced to what conditions would make, say, Minmax, optimal.
Post by Juho LaatuSome more words on trading clone independence and
Smith. Note that Minmax doesn't trade them away
since it respects them almost always. (And in these
cases we can diecuss if it is justified to violate
these criteria in these special cases.) A less than
100% compliance with some criteria may sometimes be
useful. Either beneficial or acceptable because some
criteria need to be violated in any case.
That goes both ways. If Minmax respects them almost always, then wanting
a method that behaves maximally like Minmax except when doing so would
make it vulnerable to cloning (or non-Smith, or whatever), trades off
little for a large "margin of safety" gain, since the situations are
rare. Of course, the other way is what you mentioned, that if they are
rare situations, then there may not be a point in making the method more
complex just to cover them. (Then again, one should note that in the
face of an adversary, corner cases will occur more often than usual,
since the adversary will actively seek them out if they benefit it.)
Post by Juho LaatuI did'n btw quite like term "Minmax heuristic" since
my dictionary defines heuristic in mathematics,
science and philosophy as "using or obtained by
exploration of possibilities rather than by
following set rules". The rules and justifyig
explanations of Minmax(margins) are very exact.
(Actually most other Condorcet methods are more
inclined towards heuristic style exploration, e.g.
to find the most strategy resistant methods.)
Granted, though I think most Condorcet methods are rigorous. Schulze (by
the beatpath definition) would give an objective to be maximized by
reasoning that if there's a circular tie, the candidate that indirectly
beats the others is preferrable. At the election methods level,
"programs" and "functions" become very similar, and one may be phrased
in terms of the other, generally speaking; it would be hard to make a
functional description of say, first preference Copeland, or "Condorcet
else IRV".
Post by Juho LaatuPost by Kristofer MunsterhjelmIndependence of clones make the method resistant to
nomination (dis)incentives. Or rather, robust independence
of clones (not just "remove clones, then run through
method"), does. This is useful because one of the major
problems with Plurality is that it has a severe nomination
disincentive; if your candidate is similar to some other
candidate, you'll both lose. It's the other way with
Borda.
I don't quite see what you're saying. The Democrat
candidates have a clear group preference order, whereas the
50: D1>D2>D3>R1>R2>R3
16: R1>R2>R3>D1>D2>D3
17: R2>R3>R1>D1>D2>D3
17: R3>R1>R2>D1>D2>D3
A cloneproof method would act as if D* and R* are one
candidate (more or less). It may pick R3 instead of R1
because 18 instead of 16 preferred that one, but it
shouldn't switch from R* to D*.
For the example above, Ranked Pairs / MAM gives the social
ordering D1 = R1 > D2 = R2 > D3 = R3.
Yes that's what I thought except that maybe the
Democrats were neutral with respect to the
Republican candidates (D1>D2>D3>R1=R2=R3) or had
similar circular opinions as the Republican voters.
To me the interesting question is which one is
better, D1 or R1. D1 doesn't lose to anyone. R1
would lose (with the modified votes) to R3 quite
badly (i.e. the voters would like to change R1 to
R3 after R1 has been elected).
Should we then not elect the "most satisfying" D1.
Or should we strictly stick to the ideal that if
Republicans had not nominated R3 (that caused the
problems to R1) then R1 would have won (if the
votes had otherwise stayed the same).
Note that this violation of clone independence
may not be a big enough threat to the parties to
discourage nomination of more than one candidate.
I guess it would be more typical that nomination
of more than one candidate increases the
probability of that party to win the election.
(I also note that nomination of two candidates
looks still very safe from this example point
of view :-).)
Even if it had been D1 = R3 > D2 = R2 > D3 = R1, it would still have
been cloneproof. I think I see what you mean, though; in a way, it's
similar to the argument in favor of D'Hondt (as a divisor method among
others) that parties can only gain by joining - there should be a
disincentive to fragmenting.
Obviously, my example is a two-party situation, so yes, there a primary
plus plurality would probably work as well, but it's a contrived example.
Post by Juho LaatuPost by Kristofer MunsterhjelmWould there be a situation where "first from a social
ordering" and "best single winner" would be
different in a single-winner election? If so, what is that
situation? (I assume there's no tie for first place.)
No. For one need, to elect a single winner,
picking that single winner from the top of the
social ordering should make no difference. I
expect the society to determine the criteria
well, and that should point out one of the
candidate (or a tie). The tail of the social
ordering is irrelevant (i.e. one could use
different conflicting social orderings to
point out the same single winner).
Which means that one may use Kemeny, which outputs a social ordering and
minimizes a measure on potential orderings, to pick a winner (or more
generally, any such method). If the tail of the social ordering doesn't
matter, one can simply remove it afterwards (although I suppose that
could lead to people asking why the metric should be on a social
ordering scale in the first place).
Post by Juho LaatuPost by Kristofer MunsterhjelmEven with a method that permits truncation, parties may
tell voters how to vote. This happened in New York when they
used STV, and also in Ireland. Of course, there's a risk
that one'll overextend the vote management and thus lose
seats instead of gain them. Something similar could happen
with Condorcet "game of chicken" dynamics
regarding burial, if a sufficiently large group starts
burying. We don't have any data on the likelihood of
single-winner "vote management" (party-directed
strategy), though, simply because preferential single-winner
methods haven't been used long enough.
I see Condorcet methods as excellent methods if
the level of strategic voting stays at random
noise level. If majority of the voters start
voting strategically, either in their own style
or (worse) based on centrally coordinated
strategies then I'd be willing to consider
moving to use some other methods with which
this particular society would work better
(maybe down to Plurality and wait for things
to settle). It is however quite probable that
in many societies Condorcet methods would work
fine (including Minmax).
I would rather have a Condorcet method on the strategy side of the
Pareto front than plain old Plurality; or if the society's so interested
in strategizing, use DSV Approval and set the human "grandmasters"
against computers. That might be too complex, however, but would be a
fair version of what might happen in any case if the base method allowed
optimization/strategy: various parties would start using computers to
find the ideal strategic vote.
Post by Juho LaatuPost by Kristofer MunsterhjelmWell, yes, but would the people? Of those that agree that
nonmonotonicity is a problem, would most also consider
reversal symmetry of no great importance? In the worst case,
people wouldn't understand Arrow at all, and the various
groups could end up using that to fling criterion failures
at each other.
We have seen that it is easy to generate all
kind of bad examples, violations of nice
looking criteria, biased terminology, and to
ignore some of the weak spot's of one's own
favourite method, and to emphasize different
points in the right way. Election methods are
complex enough and the example cases
interesting enough to do this. For this
reason I mentioned the unified front of
respected experts. Maybe solutions like
Wikipedia would work too, but also there
I see lots of black and white for and
against opinions. Maybe we are also lacking
a scientific method based community of
practical implementation related election
method research with a popularization arm.
That's a good idea, and I think it would be useful if we were to move to
an advocate stage. Create or find a group that's sufficiently scientific
to understand the question and the methods, yet sufficiently independent
to say "this seems best to me" outside of the context of EM messages.
The other aspect of the method would be simplicity and the relative
importance of criteria (how easy it would be to popularize, and what
obstacles it may face from opponents), and that aspect would be more
readily answered by potential voters (ordinary people), as those are
after all who would be using whatever method one would focus on advocating.
Post by Juho LaatuPost by Kristofer MunsterhjelmPost by Juho LaatuI'd appreceate e.g. a web site that would aim at
neutral description of all the relevant methods
(plausible candidates for election reforms), with
estimates on how they would perform in real life.
How would we get those estimates? By testing the methods?
Since there can be many kind of tests with many
kind of simplification and bias I'd trust also
here a team of trusted experts or a scientific
community with strong emphasis on seeking best
results with respect to practical applicability
of the results in real life.
Tests are often just very basic artifical models
of real life situations. Therefore they need to
be interpreted. And here we may need to trust
the expert group or community to focus on the
relevant aspects.
Yes, though simulations can be contentious. Consider, for instance,
Bayesian regret.
Post by Juho LaatuI btw trust also on simple example cases. They
are useful in demonstrating how probable the
benefits and vulnerablities are in real life.
Yee diagrams are good here, I think. The situations they model are ones
that could practically happen; it's a lower bound of sorts - if a method
shows odd results there, it would be suspect, but the converse may not
be true.
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