[EM] Detailed stats for the ordinal methods

[Closed Limelike Curves]

I'm thinking more along the lines of Burt Monroe's nonelection of
irrelevant alternatives. He shows Nanson, Baldwin, and any system
equivalent to Minimax in the 3-candidate case fails the Condorcet criterion
with strategic voting.

On Sun, May 12, 2024 at 8:27 PM Michael Ossipoff <email9648742 at gmail.com>
wrote:

>
>
> 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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