[EM] Semantics of voting

[Kristofer Munsterhjelm]

On 01.03.2022 18:03, Colin Champion wrote:
> I started drafting a post on this subject, but it got longer and longer
> so I turned it into a web page:
> http://www.masterlyinactivity.com/condorcet/semantics.html

>    Briefly, I argue that discussions of voting methods are only
> meaningful if a semantics can be attached to the correctness of
> electoral decisions; that models (such as jury and spatial models) can
> provide such a semantics, leading to a Bayesian interpretation of
> correctness; that the logical criteria stand or fall according to
> whether they can be validated under a suitable semantics; that some
> stand, some fall, and some are best seen as statistical approximations.
>    The topics I discuss are ones I have not seen addressed elsewhere. I
> have no idea how new my ideas are, or whether, if I was better grounded
> in the field, I'd have been able to discuss the subject with greater
> wisdom.

The closest thing I know of are the frequentist approaches to modeling
election methods, e.g. Kemeny as MLE of a certain extension of the model
in Condorcet's jury theorem, and generalizations to this approach (e.g.
https://www.jstor.org/stable/41106629).

Bayesian statistics is not my field, but as I understand your page,
you're trying to show whether certain models can naturally result in
monotonicity and participation failures, similar to how e.g. IIA by
necessity arises from every ordinal method.

The idea of trying to recover the statistical parameters of issue space
and then electing the best candidate is a good one; I think the reason
there hasn't been much of it is that voting methods research has been
more focused on strategy and on pass-or-fail criteria.

Do there exist extensions to Bayesian stats that handle cases where the
input data may be adversarially corrupted by some party who seeks to
confuse the process? That'd be like voting method strategy.

There's also the issue of noise. In your tetrahedron vs line example,
it's possible that one of the voters filled in the ballot incorrectly
(or misjudged or something). But I imagine that "ordinary" Bayesian
stats could handle noise with appropriately broad priors.

I also think that some properties are considered as "embarrassment
criteria", as in: it seems illogical that a method should fail this
particular criterion, and the opponents of the method might use this to
ridicule the method, so we better patch it up. Or it may be part of how
we think a voting method should behave, no matter what.

Binary properties give a certain guarantee that if something strange
happens, it won't be of this particular type. Let's say, for instance,
that we want to generalize majority rule. And suppose that under a
particular model (jury, say), Borda is optimal. Then if we want to
uphold majority rule no matter what, but still want some performance on
jury models, then Black may be a better choice than Borda.

In a way, there's always a question of what matters.

But looking closely into how VSE might be optimized by Bayesian methods
and how certain spaces imply certain properties is definitely
worthwhile, I think :-)

-km