Quadratic Voting in Finite Populations

34 Pages Posted: 28 Feb 2015 Last revised: 29 Dec 2019

See all articles by Bharat Chandar

Bharat Chandar

Stanford Graduate School of Business

E. Glen Weyl

Microsoft ; RadicalxChange Foundation

Date Written: December 28, 2019

Abstract

We study the performance of the Quadratic Voting (QV) mechanism proposed by Lalley and Weyl (2016) 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 numerical game theory methods with statistical limit results to computationally approximate equilibria for moderate population sizes. Finally, we use purely numerical 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, with the analytic bounds on potential welfare typically 1.5 to 3 times more conservative than the results from numerical calculation. In our most precise results, we have not found an example where QV sacrifices more than 10% of potential welfare for any population size. However, we find scenarios in which one-person-one-vote rules outperform QV and also show that convergence to full efficiency in large populations may be much slower with fat tails than with bounded support. The results suggest that in highly unequal societies, 1p1v or QV with artificial currency may give superior efficiency to QV with real currency.

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

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

Suggested Citation

Chandar, Bharat and Weyl, Eric Glen, Quadratic Voting in Finite Populations (December 28, 2019). Available at SSRN: https://ssrn.com/abstract=2571026 or http://dx.doi.org/10.2139/ssrn.2571026

Bharat Chandar

Stanford Graduate School of Business ( email )

Stanford, CA
United States

Eric Glen Weyl (Contact Author)

Microsoft ( email )

306 Park Ave
Apt 3
Hoboken, NJ 07030
United States
8579984513 (Phone)

HOME PAGE: http://www.glenweyl.com

RadicalxChange Foundation ( email )

HOME PAGE: http://www.radicalxchange.org

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