Voting by Simultaneous Vetoes

We design voting mechanisms in which every Nash equilibrium is coalition proof, preventing the well known coordination failures of usual voting systems. In each of these simultaneous mechanisms, each voter has the right to select a list of alternatives to veto, and the winner is selected randomly from the nonvetoed alternatives. For each specification of the veto rights, we show that each of these mechanisms implements a veto by random priority rule introduced by Moulin[1981]. We then discuss necessary conditions for arbitrary mechanisms to satisfy implementation in both Nash and coalition proof and show that the existence of veto rights in the mechanism is unavoidableto achieve this demanding implementation notion.