[EM] Semantics of voting

[Kevin Venzke]

Hi Colin,

Le mardi 1 mars 2022, 11:04:13 UTC−6, Colin Champion <colin.champion at routemaster.app> a écrit : 
> 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.

I read through this a few times. I think I understand most of it, other than the
demonstrations, which will probably be my own failing.

It seems like your main stance is that even if we assume that all votes are
sincere, we should still have a theory about where the rankings come from, if we
want to talk about how a method ought to behave.

Maybe this line of thinking can be seen in Yee diagrams, where no strategy is
considered and methods are judged as to whether win regions match the Voronoi
diagram.

I may not understand free variables vs. bound variables. It sounds like with
bound variables, some standard is "right" if it tends to be right. While free
variables would judge standards to be right or wrong in every specific case.

So you say that a unanimity (or Pareto) criterion would be unjustified under
free variables with a jury/valence model. While I can see that most standards
might be unusable with free variables, in the case of unanimity I don't see how
it could be unjustified. When you discuss IIA it sounds like the jury/valence
model is essentially an underlying ranking for each voter, with no issue space.
Is there an assumption that a voter's ranking can be wrong in some sense?

If so, does that also apply to the spatial model? (i.e. that the voter is not
placed correctly in space.)

I think it's curious that when you bring in "external facts," in both ways
you've done this, those facts would tell you who the best candidate is in any
given case. There's no ambiguity. Could we have external facts that don't
necessarily do this? That wouldn't necessarily be useless, since we could at
least discuss phenomena in the new terms instead of just on the cast ballots.

What if we think that no model of external facts is justifiable in some
environment? Can we say nothing then? Maybe our conclusions would reveal some
implicit assumptions, I suppose, indicating something about what we suspect the
external facts are.

If the model must tell us the winner (due to one's definition of what a model
is), I wonder what stops a Condorcet advocate from copy/pasting the cast ballots
as external facts and declaring that the Condorcet winner within the external
facts is the targeted, right winner.

When you discuss the validity of Participation under a spatial model, do you
consider whether the transformations envisioned by the criterion can actually
be achieved under the model? Perhaps there could be a gray area of satisfaction
where we say a method fails a criterion, but only if the underlying model is
wrong (or e.g. if voters are insincere).

I don't understand your criticism of the notion that Participation "relates ...
to additional incentives offered to voters." Some of us, and Woodall, do
recognize Participation as a monotonicity criterion, for what it's worth. But I
don't know how to explain the strategic implications except in terms of
incentives offered to voters.

When you discuss IIA I am a little confused. You seem very against it, but only
discuss the jury/valence model. Is it simply obvious that it also applies to the
spatial model? What you say is that it's "clearly invalid under a Bayesian
semantics" which seems like an even broader claim.

In order to discuss IRV, you say that if we are willing to accept monotonicity
as a "valid" criterion under the model, then we can use it to judge the accuracy
of methods.

I expect there are three possibilities for a proposed criterion and model.
Either the criterion is valid (i.e. necessarily true), or it's incompatible, or
it's orthogonal, non-contradictory. In the case of Participation under a spatial
model, you say this "cannot be valid." I guess you showed it's incompatible.

What do you suppose is the status of a criterion in the middle state, neither
incompatible nor necessarily true? Must we be indifferent to it, having
exhausted the only legitimate method of assessing it?

Somewhat related to this, you point out that Borda is ideal or near ideal under
the jury model. But almost no one actually advocates Borda, for, let's say,
reasons of strategy. The model can't speak to these reasons, or at least, can't
ultimately offer us anything but an insistence that we use a Borda-like method.
I find that disturbing, since the model is what we're using to gauge potential
properties and that seems like its whole point.

Kristofer mentioned "embarrassment criteria" as an issue. I will often consider
a criterion important because I think that other people think it's important.
This results in a lot of subjectivity. For example maybe we can quantify
monotonicity failure, but how much is too much? Difficult to see a way out of
this.

Kevin