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Published in: Public Choice 1-2/2021

11-11-2020

Will quadratic voting produce optimal public policy?

Authors: John C. Goodman, Philip K. Porter

Published in: Public Choice | Issue 1-2/2021

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Abstract

Under quadratic voting people are able to buy votes with money. The claims that rational voters will make efficient electoral choices rest on assumptions about how voters acquire and share information. Specifically, that all voters share common knowledge about the probability that any one of them will be the decisive voter, but do not (appear to) share knowledge in any specialized way within special interest groups. This paper asserts that quadratic voting is no more likely to promote efficiency than the current system of one-person-one-vote. Information costs are critical. If information is costly, organized interest groups on either side of an issue provide low-cost information to their members and sharing common knowledge across groups is less likely. Then, small differences lead to large welfare losses. If information is free, special-interest groups provide opportunities for collusion that undermines the efficiency of quadratic voting. Even if collusion could be prevented, the dual uses of money to buy votes and to disseminate information organizes interest groups as if their members were colluding. The role of information and the fact that voting is not costless create efficiency biases under quadratic voting that favor political organization and concentrated values. To the extent that these attributes are overrepresented in the present system, quadratic voting will only make it worse.

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Footnotes
1
A generalization of this finding is proposed by Tideman and Plassmann (2017), who argue that no social choice mechanism is likely to be efficient unless “all parties involved … bear the marginal social costs of their actions.”
 
2
Weights depend on the distribution of benefits within the group.
 
3
Some of the problems, including collusion and voter misinformation are discussed by Weyl (2017).
 
4
Without equilibria, the idea of efficiency is moot.
 
5
From Eq. (1) and consistent with free riding in large groups, we know that λ will be very small. For visual effect, we have assumed that\(\lambda^{P} = 1/4\) and \(\lambda^{O} = 1/2\), since only the ratio matters in determining the political outcome, Qe.
 
6
Lalley and Weyl (2018) address voting costs, collusion and different perceptions of the probability of casting the decisive vote. Their focus is on preserving the efficiency properties of quadratic voting and they demonstrate the robustness of quadratic voting over a wide range of assumption about the distribution of voters, their preferences and their perceptions of being the decisive voter. We have the opposite focus. We draw attention to the same phenomenon that leads to special interest dominance in voting models: concentrated versus dispersed benefits, collusion with heterogeneous versus homogeneous preferences and persuasion as well as the expanded role of money in determining the political outcome.
 
7
It can be shown that Xi = M/N maximizes \(\sum\nolimits_{i = 1}^{N} {X_{i}^{{\frac{1}{2}}} }\), subject to \(M = \sum\nolimits_{i = 1}^{N} {X_{i} }\) for all i.
 
8
Let m=M/N be the optimal allocation of M within an interest group and consider any unequal distribution m+δ and m − δ (0<δ<m) between two members. Collusive allocation of m yields \(2\sqrt m\) votes for the two individuals and the alternative allocation yields \(\sqrt {m + \delta } + \sqrt {m - \delta }\) votes. Collusion then gains \(G = 2\sqrt m - \sqrt {m + \delta } - \sqrt {m - \delta } > 0\) votes and the amount of votes gained by collusion increases with increases in variation, δ, because \(\partial G/\partial \delta = 2\delta (m^{2} - \delta^{2} )^{{ - \frac{1}{2}}} > 0\).
 
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Metadata
Title
Will quadratic voting produce optimal public policy?
Authors
John C. Goodman
Philip K. Porter
Publication date
11-11-2020
Publisher
Springer US
Published in
Public Choice / Issue 1-2/2021
Print ISSN: 0048-5829
Electronic ISSN: 1573-7101
DOI
https://doi.org/10.1007/s11127-019-00767-4

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