[EM] Manipulability stats for (some) poll methods

[Closed Limelike Curves]

>
> I think part of this can be answered by thinking about just what the
> manipulability measure, well, measures. It gives an indication of how
> well the method protects the honest outcome against strategy by the voters.
>
Right; that's largely my concern. It's also why I'm concerned about
blasting emails to the EM list saying stuff like "RANKED PAIRS HAS A 50%
MANIPULATION RATE, AND IRV HAS A 7% RATE", given this list includes lots of
people who are less involved in these discussions and don't know
manipulability is a very narrowly-defined measure of strategy-resistance.

A good example of this is James Green-Armytage's papers or Tideman's book
on this topic. I constantly have to deal with people who think his
studies show IRV is "93% STRATEGYPROOF" and every other method "collapses"
under strategic voting. (When systems like score, approval, etc. react
quite well to strategy, because they behave like maximal lotteries.)

Manipulation rate is like a p-value. It's a somewhat-meaningful metric that
can be useful when handled delicately by an expert. The issue is it
sounds *very
*similar to a different, much more important, question like "how well will
this method react to strategic voting". It's not that important to know
whether it's theoretically possible, given perfect information and
coordination, to manipulate the election; much more interesting are
questions like "what happens at the strategic equilibria" and "how robust
are those equilibria when we fiddle with the assumptions".

I'm also kinda interested in behavior with different kinds of strategy. I
think voters are about equal-parts expressive, level-strategic (they care
about how high the candidates' scores are, e.g. people who turned out in
France 2003 because they wanted to show France had "rejected" Le Pen), and
winner-strategic.

On Tue, May 14, 2024 at 8:59 AM Kristofer Munsterhjelm <km_elmet at t-online.de>
wrote:

> On 2024-05-03 23:18, Michael Ossipoff wrote:
> > Then Plurality is better than Black & Score; & Benham & Woodall are no
> > better than IRV; & IRV is 4 times better than the best Condorcet methods?
> >
> > Of course JGA’s results lead to similar questions.
> >
> > Doesn’t this bring into question the meaningfulness & usefulness of
> > manipulability as a measure of merit?
> >
> > IRV has an incomparably worse strategy problem than the best Condorcet
> > methods.
> >
> > Plurality is incomparably strategically worse than Approval.
> > Benham & Woodall, as everyone would agree, significantly improve on IRV.
>
> I think part of this can be answered by thinking about just what the
> manipulability measure, well, measures. It gives an indication of how
> well the method protects the honest outcome against strategy by the voters.
>
> IRV vs Benham does look strange, and I would like to investigate it
> further when I have the time. For instance, it's difficult to reconcile
> IRV's problems with not electing Condorcet winners with its low
> strategic susceptibility (since the existence of an unelected CW is a
> strategy opportunity).
>
> Some of IRV and Plurality's problems come from their strategic
> nomination incentive, which my stats don't capture. And another part of
> the problem is that, even if IRV and Benham are equally good at
> defending the honest outcome, IRV's honest outcome is much worse than
> Benham's to begin with. (Similarly, Approval and the manipulable
> Condorcet methods have better honest outcomes than Plurality.)
>
> But the broader patterns seem to be more understandable.
>
> That Approval and Score are on the high end makes sense to me because
> strategy (watching the polls) is such an integral part of the greater
> dynamic. Anybody who looks at the polls and then focuses his cutoff to
> maximize the effect will have a good chance of changing the outcome, and
> reducing a fully ranked non-dichotomous ballot down to an approval-style
> ballot to begin with is somewhat of an art.
>
> Someone on reddit said: "I would never vote in an Approval election
> without reviewing all the polls, but wouldn't care in a Baldwin's
> election. It's not really about the raw complexity of the strategies
> itself, but their relevance."
>
> So what I would take from the manipulability values is that we should
> try to find a method that both has good honest outcomes, and is
> resistant to strategy away from those honest outcomes. IRV fails the
> former; the cardinal methods fail the latter.
>
> Someone might say "just sum up the utility of the worst candidate that
> could be elected by strategy, then". But I think that there's a drawback
> to strategy in itself. Intuitively "you shouldn't need to look over your
> shoulder all the time". Just the effort of adapting your vote to the
> strategy can deter.
>
> (And there's value in having few strategies available, because then
> there are fewer ways things a misjudged strategy could blow up in
> everybody's face.)
>
> -km
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>
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