# [EM] Semantics of voting

Kevin Venzke stepjak at yahoo.fr
Tue Mar 8 16:14:27 PST 2022

```Hi Colin,

> My notion of a jury model is that each candidate has an objective
> valence (or excellence), which we can take to be gaussianly distributed,
> and that each voter ranks candidates according to his or her own noisy
> estimates of their valences. This is essentially the model Peyton Young
> used, except that he worked with probabilities rather than with
> statistical distributions. (I prefer my own approach because I find it
> hard to keep a clear head when dealing with probabilities. I'm not sure
> Young himself entirely succeeded - I think at one point he says
> "independent" when he means "conditionally independent given... ".)

Ok. A sort of hidden rating, and the voters use them to populate whichever type
of ballot is provided.

> I'm quite struck by my counterexample to IIA (49% A>C>B, 51% B>A>C,
> which is simply a numerical version of Good's argument). It seems to me
> obvious that A is the rightful winner, and that if C is removed from the
> ballots then B becomes the rightful winner. Certainly anyone who thinks
> that C simply drops out of the analysis, and that my example is
> equivalent to 49% A>B, 51% B>A is making an elementary statistical
> error. I cannot believe that Arrow would have made such a mistake, so I
> conclude that he understood electoral correctness in a different sense
> than Good and I do. If only he had told us what it was!

Doesn't IIA hold *within* a jury model? I mean the estimates of valences.
Perhaps Arrow intends such a model, and means that it would be reasonable to
hope that a property of the model could also be reflected in the procedure.

> I agree that the Borda count is hopeless in the presence of tactical
> voting, even under a jury model. But philosophically I don't feel
> threatened by this. My view is that the right electoral decision is the
> one which is most likely to give the best candidate, or whose expected
> loss is least, or whatever, given - simultaneously - a model of sincere
> voting behaviour and a model of how voters try to beat the system.

My view is pretty similar.

Kevin
```