Here's a proof of part (f): In phase II if my ballot is not one of the ones drawn, then it has no influence.
So suppose that it is one of the drawn ballots. If all of the drawn ballots, including mine, approve the phase I winner, then she is elected., and my utility for the result is exactly what I ascribe to her. In the other case, the winner is my favorite (if my ballot is the first drawn) or the benchmark lottery winner (if my ballot is not the first drawn). And since the number of ballots drawn is at least five, the result follows. > f) If every voter i prefers the compromise option W to a lottery in> which i's favourite is elected with 20% probability and the Random> Ballot lottery is applied with 80% probability, and all voters > know that> this is the case, then it is likely that all voters will say > "yes" in> phase II and W will be the sure winner.> ---- Election-Methods mailing list - see http://electorama.com/em for list info