Nash Equilibria for Quadratic Voting

56 Pages Posted: 30 Aug 2014 Last revised: 18 Jul 2019

See all articles by Steven Lalley

Steven Lalley

Department of Statistics, University of Chicago

E. Glen Weyl

Microsoft ; RadicalxChange Foundation

Date Written: July 16, 2019


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.

Keywords: social choice, collective decisions, large markets, costly voting, vote trading, Bayes-Nash equilibrium

JEL Classification: C72, D71, D82, H41

Suggested Citation

Lalley, Steven and Weyl, Eric Glen, Nash Equilibria for Quadratic Voting (July 16, 2019). Available at SSRN: or

Steven Lalley

Department of Statistics, University of Chicago ( email )

Eckhart Hall Room 108
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Eric Glen Weyl (Contact Author)

Microsoft ( email )

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RadicalxChange Foundation ( email )


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