You’ll never believe what happened to me the other… err. Sorry, wrong post.
So I read this paper the other day: http://www.votingmatters.org.uk/ISSUE26/I26P3.pdf
It’s a good idea. Essentially the idea is you apply the maximum entropy principle to probabilistic voting systems: You take the distribution on Perm(Candidates) which maximises entropy subject to the constraints P(x < y) = fraction of the voters who think x < y. This is satisfiable because random dictator has these constraints. The biggest problem with it is that it requires you to do a linear optimisation problem in N! - 1 dimensions, which isn't great. Additionally, I'm mainly interested in randomized methods for single-winner elections, which have a much smaller number of dimensions. I was wondering if there was a natural analogue to the idea for this case. Can anyone think of one? Obviously you can consider the maximum entropy distribution on Candidates, but it's not obvious what the equivalent constraints should be. Thoughts?