Journal Of The Econometric Society

An International Society for the Advancement of Economic
Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: Nov, 2019, Volume 87, Issue 6

Linear Voting Rules
p. 2037-2077

Hans Peter Grüner, Thomas Tröger

How should a society choose between two social alternatives if participation in the decision process is voluntary and costly, and monetary transfers are not feasible? Assuming symmetric independent private values, we show that it is utilitarian‐optimal to use a linear voting rule: votes get alternative‐dependent weights, and a default obtains if the weighted sum of votes stays below some threshold. Any combination of weights and threshold can be optimal. A standard quorum rule can be optimal only when it yields the same outcome as a linear rule. A linear rule is called upper linear if the default is upset at every election result that meets the threshold exactly. We develop a perturbation method to characterize equilibria of voting rules in the case of small participation costs and show that leaving participation voluntary increases welfare for any two‐sided upper linear rule that is optimal under compulsory participation.

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Supplemental Material

Supplement to "Linear Voting Rules"

This online appendix contains material not found within the manuscript.