The Structure of Strongly Monotonic Probabilistic Voting Procedures.

Pattanaik and Peleg showed that the power structure under a probabilistic voting procedure which satisfies regularity, ex-post Pareto optimally and independance of irrelevant alternatives is almost completely characterized by random dictatorship. Their characterization is not complete because it requires some additional conditions. We propose a new probabilistic monotonicity axiom called strong monotonicity and show that, if the probabilistic voting procedure is required to satisfy this new axiom along with their 3 axioms, then the distribution of coalitional power under it is completely characterized by random dictatorship.