Kevin – I suspect we don't disagree about anything. It would have been clearer if I'd said that my jury model was a special case of the Condorcet/Young model with added distributional assumptions for my own conceptual convenience.    A simpler example of IIA has occurred to me which I mention for what it's worth. It doesn't refer to voting but brings in all the important features.    Let x, y and z be 3 values. We have no idea which is greater than which. Our initial beliefs can be expressed by giving them independent standard Gaussian priors. E[x-y]=0.    Now we're given a single piece of information that x>z. Our posterior beliefs about y are unchanged from our prior, but we now have a joint posterior distribution on (x,z) which is a standard bivariate Gaussian restricted to the half-plane in which x>z. E[x]>0, E[z]<0; E[x-y]>0.    Here x is the merits of automobiles, y is the merits of buses, and z is the merits of teleportation. If we are interested in choosing between automobiles and buses then teleportation is an irrelevant alternative; according to IIA comparisons with an irrelevant alternative can be of no help in choosing between automobiles and buses; Bayes' theorem disagrees.    Colin On 09/03/2022 00:14, Kevin Venzke wrote: > 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