The Efficiency of Quadratic Voting in Finite Populations

26 Pages Posted: 28 Feb 2015  

E. Glen Weyl

Microsoft Research; Yale University

Date Written: February 26, 2015


We study the performance of the Quadratic Voting (QV) mechanism proposed by Lalley and Weyl (2015) in finite populations of various sizes using three decreasingly analytic but increasingly precise methods with emphasis on examples calibrated to the 2008 gay marriage referendum in California. First, we use heuristic calculations to derive conservative analytic bounds on the constants associated with Lalley and Weyl’s formal results on large population convergence. Second, we pair computational game theory methods with statistical limit results to approximate equilibria for moderate population sizes. Finally, we use purely computational methods to analyze small populations. The more precise the methods we use, the better the performance of QV appears to be in a wide range of cases. In our most precise results, we have not found an example where QV sacrifices more than 4% of potential welfare for any population size.

Keywords: Quadratic Voting, small populations, analytic approximations, computational game theory

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

Suggested Citation

Weyl, E. Glen, The Efficiency of Quadratic Voting in Finite Populations (February 26, 2015). Available at SSRN: or

Eric Glen Weyl (Contact Author)

Microsoft Research ( email )

641 Avenue of the Americas
7th Floor
New York, NY 10011
United States
(857) 998-4513 (Phone)


Yale University ( email )

28 Hillhouse Ave
New Haven, CT 06520-8268
United States

Paper statistics

Abstract Views