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.
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.