My suspicion is that this just corresponds to some particular rule for normalizing preferences over strategies.
Yes, assuming that the delegates always take any available Pareto improvements, it should work out to that [edit: nevermind; I didn’t notice that owencb already showed that that is false]. That doesn’t necessarily make the parliamentary model useless, though. Finding nice ways to normalize preferences is not easy, and if we end up deriving some such normalization rule with desirable properties from the parliamentary model, I would consider that a success.
Harsanyi’s theorem will tell us that it will after the fact be equivalent to some normalisation—but the way you normalise preferences may vary with the set of preferences in the parliament (and the credences they have). And from a calculation elsewhere in this comment thread I think it will have to vary with these things.
I don’t know if such a thing is still best thought of as a ‘rule for normalising preferences’. It still seems interesting to me.
Yes, that sounds right. Harsanyi’s theorem was what I was thinking of when I made the claim, and then I got confused for a while when I saw your counterexample.
Yes, assuming that the delegates always take any available Pareto improvements, it should work out to that [edit: nevermind; I didn’t notice that owencb already showed that that is false]. That doesn’t necessarily make the parliamentary model useless, though. Finding nice ways to normalize preferences is not easy, and if we end up deriving some such normalization rule with desirable properties from the parliamentary model, I would consider that a success.
Harsanyi’s theorem will tell us that it will after the fact be equivalent to some normalisation—but the way you normalise preferences may vary with the set of preferences in the parliament (and the credences they have). And from a calculation elsewhere in this comment thread I think it will have to vary with these things.
I don’t know if such a thing is still best thought of as a ‘rule for normalising preferences’. It still seems interesting to me.
Yes, that sounds right. Harsanyi’s theorem was what I was thinking of when I made the claim, and then I got confused for a while when I saw your counterexample.