[EM] Detailed stats for the ordinal methods

[Michael Ossipoff]

On Sun, May 12, 2024 at 19:56 Closed Limelike Curves <
closed.limelike.curves at gmail.com> wrote:

[quote]

 I’d  conjecture no plurality-Condorcet method (pairwise defeats of <50%
are allowed) is actually Condorcet in the presence of strategy.
[/quote]

A very safe conjecture, if you’re conjecturing that the CW won’t win every
strategic circular tie.  :-)

How would anyone expect the CW to always win in every strategic
circular-tie?

 But the Condorcet Criterion doesn’t require that.

In one form, it’s defined for sincere voting & certain preferences. In
another form, it’s defined by who should win if someone pairbeats everyone
else, by the ballots. The latter definition requires a specification about
the balloting.

So you’re expounding to us about what’s Condorcet-complying, based on your
confusion about what the Condorcet Criterion says.

 No method is guaranteed to elect the CW if someone makes a strategic
circular-tie.

But the wv Condorcet methods deter offensive-strategy so well that they
achieve the ideal of no need for defensive-strategy.

If you’re the one who said that people might do offensive strategy anyway,
an analysis of the likely result is the strategist’s business.the whole
point 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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