Jury theorems with multiple alternatives

摘要

I consider a game in which imperfectly informed jurors vote to select one of several possible choices when there is a natural ordering of the possibilities. Each juror votes for the largest alternative the juror would like to implement, and the alternative that is selected is the largest alternative supported by a given number of jurors. For non-unanimous voting rules, the probability of a mistaken judgment goes to zero as the number of jurors goes to infinity. I also give necessary and sufficient conditions to obtain asymptotic efficiency under unanimous voting rules, and show that unanimous rules may lead to a bias in which moderate outcomes are never chosen.