Today I gave my first paper to the Nuffield seminar. My paper was a quite technical one, including an evaluation of Arrow's conditions - posted here, here and here.
I'd already had apologies from David, and a few other people, so in fact there weren't too many there. I don't think it's personal though - I remember attendance dropping off like this last year, what with MPhil exams and nice weather amongst other factors (the moral philosophy seminar later this afternoon was also somewhat sparser than usual).
Thanks to those who did attend - I got some very useful and constructive comments, which will keep me busy for a while (though I already have several plans for the summer, including the Brave New World paper as soon as term ends). Particular thanks to Clare Chambers, and Keith Dowding who gave me a couple of his own papers to look at.
Ben, if you show that lottery voting satisfies all of Arrow's conditions, haven't you shown that there is an error in his proof that no voting method is possible that satisfies all his conditions?
ReplyDeleteAlas, but:
ReplyDelete1) I think lottery-voting technically violates IIA.
2) Some people have argued it also violates non-dictatorship (though I'm less sure of this)
3) I've had pressed upon me the need to distinguish between Arrow's concern - welfare functions (or orderings) - and decision-mechanisms. Something I think I'd pressed against you, when I said I'm not sure Arrow cares about the mechanics of how the vote happens (e.g. writing xPy on ballot papers), but perhaps hadn't taken sufficiently seriously myself.
Unfortunately, one can't produce a counter-example to a proven theorem. There are plenty of problems lottery-voting does solve, however - e.g. it's strategy-proof.