[EM] Manipulability stats for (some) poll methods

[Kristofer Munsterhjelm]

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