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Quadratic Voting

34 Pages Posted: 13 Feb 2012 Last revised: 19 Dec 2016

Steven P. Lalley

Department of Statistics, University of Chicago

E. Glen Weyl

Microsoft Research; Yale University

Date Written: December 16, 2016


We propose Quadratic Voting (QV) as a method for binary collective decision-making: individuals buy votes for their preferred alternative, paying the square of the number of votes purchased. Quadratic cost uniquely makes the marginal cost proportional to votes purchased, encouraging voting proportional to the value and thus maximizing welfare. Similar heuristic arguments and experiments suggest it is more robust than other efficient mechanisms and it grows naturally from a variety of ideas in disparate literatures. Nonetheless, formal analysis beyond simple examples has proved illusive. By explicitly characterizing the subtle statistical structure of equilibrium, we prove convergence towards optimality in large populations in a canonical environment.

The online appendix for "Quadratic Voting" may be found here:

Keywords: social choice, collective decisions, large markets, costly voting, vote trading

JEL Classification: D47, D61, D71, C72, D82, H41, P16

Suggested Citation

Lalley, Steven P. and Weyl, E. Glen, Quadratic Voting (December 16, 2016). Available at SSRN: or

Steven Lalley

Department of Statistics, University of Chicago ( email )

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Eric Weyl (Contact Author)

Microsoft Research ( email )

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Yale University ( email )

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