[EM] Detailed stats for the ordinal methods

[Closed Limelike Curves]

> The narrow sense of turkey elections - exploiting nonmonotonicity to do
> pushover - must, for ordinal methods, belong to the "Other" strategy
> category.
>
Right, that makes sense. I was thinking of turkeys just in the sense of
"very bad candidates who win because of strategic voting". So my
real question is, what happens if voters actually play strategically? We
know for score the answer is "we end up with a Condorcet method" (from
Myerson and Weber). By contrast, I'd conjecture no plurality-Condorcet
method (pairwise defeats of <50% are allowed) is actually Condorcet in the
presence of strategy.

On Sat, May 11, 2024 at 1:48 PM Kristofer Munsterhjelm <km_elmet at t-online.de>
wrote:

> On 2024-05-09 23:56, Closed Limelike Curves wrote:
> > Hi Kristofer! Thanks for this :)
> >
> > I do want to ask though, do you think the rate of manipulable elections
> > is a good measure of the "general strategy resistance" of an electoral
> > method? The resistant set certainly seems to reduce that rate, but for
> > all I know that 7.5% is all turkey-elections.
>
> The narrow sense of turkey elections - exploiting nonmonotonicity to do
> pushover - must, for ordinal methods, belong to the "Other" strategy
> category. Not every Other strategy need to be pushover, but pushover
> must be an Other strategy. Let's consider Resistant,Borda again:
>
> >>          Ties: 0.001 (5)
> >>          Of the non-ties:
> >>
> >>          Burial, no compromise:        123     0.0246246
> >>          Compromise, no burial:        72      0.0144144
> >>          Burial and compromise:        147     0.0294294
> >>          Two-sided:                    48      0.00960961
> >>          Other coalition strats:       1       0.0002002
> >>          ================================================
> >>          Manipulable elections:        391     0.0782783
>
> There's only one out of 4995 elections with "other" strats. So pushover
> manipulability is very low. (I've designed resistant set methods that
> seem to have no pushover at all, even though they fail monotonicity. I
> haven't been able to prove why certain resistant set constructions make
> pushover impossible, though.)
>
> I can think of two ways to formalize the broader category of
> turkey-raising as mentioned on Electowiki. They would be:
>         - Supporters of candidate A encourage a candidate C to enter, so
> that
> C>B>A voters express their honest opinion; but that makes A win instead.
>         - By making C appear to have more support than he actually does,
> supporters of candidate A trick strategic B>C>A voters to compromise for
> C. As a result, the winner changes from B to A.
>
> Neither effect is captured in my simulations: the first would be a form
> of strategic nomination, and the second is a strategic play under
> imperfect information. As the number of candidates doesn't change, and
> the simulation involves a fully honest election followed by
> full-information strategy, it doesn't capture either.
>
> Strategic nomination can indeed be a problem and should be investigated
> more closely. James-Green Armytage showed that IRV has greater exit
> incentive than the Condorcet-IRV methods do, for instance. I haven't
> written code to do this, and thus my stats don't provide any information
> about strategic nomination.
>
> Taking the second effect into account would be very difficult, as we're
> then moving into a repeated game of imperfect information. But, as a
> heuristic, if the voters know that the method has low (ordinary)
> manipulability, then it would probably be harder to get them to engage
> in a self-destructive strategy as well, since it would be harder to get
> them to engage in strategy in general.
>
> And a final caveat: if you combine a strategy resistant method with
> primaries or other parts, the composition could have turkey strategies.
> I imagine that the likelihood of this happening depends on the strategic
> nomination incentives for the method: so you could see it with IRV but
> it would be less likely with Smith-IRV.
>
> -km
>
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