Quadratic Voting

N individuals must choose between two collective alternatives. Under Quadratic Voting (QV), individuals buy vote in favor of their preferred alternative from a clearing house, paying the square of the number of votes purchased, and the sum of all votes purchased determines the outcome. Heuristic arguments and experimental results have suggested that this simple, detail-free mechanism is utilitarian efficient. In an independent private-values environment, we rigorously prove that for any value distribution all symmetric Bayes-Nash equilibria of QV converge toward efficiency in large populations, with waste decaying generically as 1=N.