<div dir="ltr"><div dir="auto">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.</div></div><div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Sun, May 12, 2024 at 8:27 PM Michael Ossipoff <<a href="mailto:email9648742@gmail.com" target="_blank">email9648742@gmail.com</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div><br></div><div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Sun, May 12, 2024 at 19:56 Closed Limelike Curves <<a href="mailto:closed.limelike.curves@gmail.com" target="_blank">closed.limelike.curves@gmail.com</a>> wrote:</div><div dir="ltr" class="gmail_attr"><br></div><div dir="ltr" class="gmail_attr">[quote]</div><div dir="ltr" class="gmail_attr"><br></div><div dir="ltr" class="gmail_attr"> I’d conjecture no plurality-Condorcet method (pairwise defeats of <50% are allowed) is actually Condorcet in the presence of strategy.</div><div dir="ltr" class="gmail_attr">[/quote]</div><div dir="ltr" class="gmail_attr"><br></div><div dir="ltr" class="gmail_attr">A very safe conjecture, if you’re conjecturing that the CW won’t win every strategic circular tie. :-)</div><div dir="ltr" class="gmail_attr"><br></div><div dir="ltr" class="gmail_attr">How would anyone expect the CW to always win in every strategic circular-tie?</div><div dir="ltr" class="gmail_attr"><br></div><div dir="ltr" class="gmail_attr"> But the Condorcet Criterion doesn’t require that.</div><div dir="ltr" class="gmail_attr"><br></div><div dir="ltr" class="gmail_attr">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.</div><div dir="ltr" class="gmail_attr"><br></div><div dir="ltr" class="gmail_attr">So you’re expounding to us about what’s Condorcet-complying, based on your confusion about what the Condorcet Criterion says.</div><div dir="ltr" class="gmail_attr"><br></div><div dir="ltr" class="gmail_attr"> No method is guaranteed to elect the CW if someone makes a strategic circular-tie.</div><div dir="ltr" class="gmail_attr"><br></div><div dir="ltr" class="gmail_attr">But the wv Condorcet methods deter offensive-strategy so well that they achieve the ideal of no need for defensive-strategy.</div><div dir="ltr" class="gmail_attr"><br></div><div dir="ltr" class="gmail_attr">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.</div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"></blockquote></div></div><div><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Sat, May 11, 2024 at 1:48 PM Kristofer Munsterhjelm <<a href="mailto:km_elmet@t-online.de" target="_blank">km_elmet@t-online.de</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">On 2024-05-09 23:56, Closed Limelike Curves wrote:<br>
> Hi Kristofer! Thanks for this :)<br>
> <br>
> I do want to ask though, do you think the rate of manipulable elections <br>
> is a good measure of the "general strategy resistance" of an electoral <br>
> method? The resistant set certainly seems to reduce that rate, but for <br>
> all I know that 7.5% is all turkey-elections.<br>
<br>
The narrow sense of turkey elections - exploiting nonmonotonicity to do <br>
pushover - must, for ordinal methods, belong to the "Other" strategy <br>
category. Not every Other strategy need to be pushover, but pushover <br>
must be an Other strategy. Let's consider Resistant,Borda again:<br>
<br>
>> Ties: 0.001 (5)<br>
>> Of the non-ties:<br>
>> <br>
>> Burial, no compromise: 123 0.0246246<br>
>> Compromise, no burial: 72 0.0144144<br>
>> Burial and compromise: 147 0.0294294<br>
>> Two-sided: 48 0.00960961<br>
>> Other coalition strats: 1 0.0002002<br>
>> ================================================<br>
>> Manipulable elections: 391 0.0782783<br>
<br>
There's only one out of 4995 elections with "other" strats. So pushover <br>
manipulability is very low. (I've designed resistant set methods that <br>
seem to have no pushover at all, even though they fail monotonicity. I <br>
haven't been able to prove why certain resistant set constructions make <br>
pushover impossible, though.)<br>
<br>
I can think of two ways to formalize the broader category of <br>
turkey-raising as mentioned on Electowiki. They would be:<br>
- Supporters of candidate A encourage a candidate C to enter, so that <br>
C>B>A voters express their honest opinion; but that makes A win instead.<br>
- By making C appear to have more support than he actually does, <br>
supporters of candidate A trick strategic B>C>A voters to compromise for <br>
C. As a result, the winner changes from B to A.<br>
<br>
Neither effect is captured in my simulations: the first would be a form <br>
of strategic nomination, and the second is a strategic play under <br>
imperfect information. As the number of candidates doesn't change, and <br>
the simulation involves a fully honest election followed by <br>
full-information strategy, it doesn't capture either.<br>
<br>
Strategic nomination can indeed be a problem and should be investigated <br>
more closely. James-Green Armytage showed that IRV has greater exit <br>
incentive than the Condorcet-IRV methods do, for instance. I haven't <br>
written code to do this, and thus my stats don't provide any information <br>
about strategic nomination.<br>
<br>
Taking the second effect into account would be very difficult, as we're <br>
then moving into a repeated game of imperfect information. But, as a <br>
heuristic, if the voters know that the method has low (ordinary) <br>
manipulability, then it would probably be harder to get them to engage <br>
in a self-destructive strategy as well, since it would be harder to get <br>
them to engage in strategy in general.<br>
<br>
And a final caveat: if you combine a strategy resistant method with <br>
primaries or other parts, the composition could have turkey strategies. <br>
I imagine that the likelihood of this happening depends on the strategic <br>
nomination incentives for the method: so you could see it with IRV but <br>
it would be less likely with Smith-IRV.<br>
<br>
-km<br>
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