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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Notes
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.”
Weights depend on the distribution of benefits within the group.
Some of the problems, including collusion and voter misinformation are discussed by Weyl (2017).
Without equilibria, the idea of efficiency is moot.
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.
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.
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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Goodman, J.C., Porter, P.K. Will quadratic voting produce optimal public policy?. Public Choice 186, 141–148 (2021). https://doi.org/10.1007/s11127-019-00767-4
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DOI: https://doi.org/10.1007/s11127-019-00767-4