[EM] Arrow/Gibbard and impossibility (Re: Scientific American and the "Perfect Electoral System")

[Kristofer Munsterhjelm]

On 2023-11-14 17:25, Toby Pereira wrote:
> As Kristofer says, minimising IIA failure (at least with ranked ballots) 
> just means using Condorcet, and I think they would all be equal in that 
> respect. However, even if there is a Condorcet winner, one could still 
> argue, at least sometimes, that there has been an IIA failure. Say there 
> are three main candidates - A, B and C. Polls suggest that it's close 
> and that there will be no Condorcet winner, but that A will likely win 
> under the particular method used. C then drops out before the election 
> causing B to win. One might call this an IIA failure.
> 
> The other question is whether C dropping out was a good thing. We went 
> from probably not having a Condorcet winner to having one as a result of 
> C dropping out. Arguably C standing gives us more information overall 
> about voter preferences. And as A would have won if C had stood, A is 
> arguably the most likely "best" winner.
> 
> So while it might be nicer to have a clear Condorcet winner, in 
> situations where it's close enough for there to be a possible cycle if 
> certain candidates stand, arguably it's better if they do stand, causing 
> the cycle and giving us more information.

I agree. If there is a cycle, it's better to have it be known.

For non-Condorcet methods like Plurality, you could have apparent ballot 
Condorcet winners that are only CWs because of the pressure the system 
puts on candidates who'd otherwise ruin the result to stay out of the way.

This is part of why I don't find FairVote's argument that IRV is good 
enough because it elects the ballot CW so often very convincing. There's 
enormous two-party inertia. And if, in addition, something bad happens 
when third parties get strong, then third parties aren't going to get 
strong.

There are definitely limits to what voting methods can do on their own, 
though. Suppose there's an upcoming election and someone, if he were to 
run and could get the vote out, would be the CW, beating all the known 
candidates. But because he doesn't have access to the required 
resources, or he doesn't know how popular his political position would 
be, or a number of other reasone, he doesn't run.

There's no way a voting method, being just a mapping from elections 
(sets of ballots) to winners or social orders, can detect that such a 
"hidden candidate" exists. In a similar way, if there's a hidden cycle 
of three very good would-be candidates, all of whom would beat every 
current candidate pairwise, the method can't detect this because it 
doesn't know that they exist.

If we want to look at IIA in such a wide context, we'd have to consider 
not just the voting method, but the surrounding dynamics as well. But at 
least the good Condorcet methods should have relatively good strategic 
entry and exit resistance, going by JGA's simulations.

-km