Nash Equilibria for a Quadratic Voting Game

Abstract

A group of N individuals must choose between two collective alternatives. Under Quadratic Voting (QV), agents buy votes in favor of their preferred alternative from a clearing house, paying the square of the number of votes purchased; the sum of all votes purchased determines the outcome. We provide the first rigorous results for this mechanism, in a canonical independent private values environment with bounded value distributions. In addition to characterizing the nature of equilibria, we demonstrate that for all bounded value distributions, the utilitarian welfare losses of the mechanism as a proportion of the maximum possible welfare tends to zero as the population size becomes large.