Strategic Voting over Strategic Proposals

PHILIP BOND, HÜLYA ERASLAN
2010 The Review of Economic Studies  
Prior research on "strategic voting" has reached the conclusion that unanimity rule is uniquely bad: it results in destruction of information, and hence makes voters worse off. We show that this conclusion depends critically on the assumption that the issue being voted on is exogenous, that is, independent of the voting rule used. We depart from the existing literature by endogenizing the proposal that is put to a vote, and establish that under many circumstances unanimity rule makes voters
more » ... le makes voters better off. Moreover, in some cases unanimity rule also makes the proposer better off, even when he has diametrically opposing preferences. In this case, unanimity is the Pareto dominant voting rule. Voters prefer unanimity rule because it induces the proposing individual to make a more attractive proposal. The proposing individual prefers unanimity rule because the acceptance probabilities for moderate proposals are higher. We apply our results to jury trials and debt restructuring. 459 460 REVIEW OF ECONOMIC STUDIES inferior to majority rule. 2,3 Specifically, while majority rule aggregates information efficiently when the number of voters is large enough, unanimity rule results in mistaken decisions. As such, when the issue being voted over is exogenous, unanimity rule is a suboptimal voting rule, and reduces the expected payoff of voters. Nevertheless, unanimity rule is used in many settings. For example, under the US Trust Indenture Act (TIA) of 1939, debt can be restructured only if all creditors agree. Likewise, unanimity is commonly required in jury trials. The results of the strategic voting literature suggest that a majority vote would be more efficient in such settings. In this paper, we show that the conclusion that majority rule is superior depends critically on the assumption that the proposal being voted over is exogenous. We do so by studying the second consequence of the voting rule mentioned above, namely that it affects the proposal being voted upon. We show that under many circumstances unanimity rule increases the expected utility of voters, because it induces the proposer to make a more attractive offer. Furthermore, in a subset of such circumstances, unanimity rule is Pareto superior, because it also increases the proposer's expected utility-even when his interests are diametrically opposed to those of the voters. At the end of the paper, we analyse two specific applications: jury trials and debt restructuring. We consider the following setting. One individual, the proposer, makes a take-it-or-leave-it offer to a group. The group members, the voters, must collectively decide whether to accept or reject the offer, and we assume they do so by holding a vote. The fraction of votes required to accept the proposer's offer is fixed prior to the offer (by, e.g. law, contract, or the common consent of voters). As such, when the proposer makes his offer he takes the voting rule as given. We follow the strategic voting literature and focus on information aggregation when the number of voters is large. As one would expect, and regardless of the voting rule, the acceptance probability is increasing in the attractiveness of the offer to voters. We assume there is sufficient conflict between the proposer and voters that the proposer faces a trade-off between a high offer that is accepted more often and a low offer that is accepted less often. Equilibrium offers are determined by this trade-off. As in the prior literature, the group (asymptotically) makes the correct decision under majority rule but makes mistakes under unanimity rule. In particular, voters reject low offers more often than they should, and accept high offers more often than they should. Provided the proposer's payoff under disagreement is not too low, the mistakes that arise under unanimity rule benefit voters. In this case, when facing voters using majority rule, the proposer is not willing to make a high offer, but rather prefers a smaller offer accepted less often. Because voters make mistakes under unanimity rule by rejecting low offers more often than they should, the proposer responds by offering more than he would under majority rule. Put slightly differently, voters would like to commit to reject low offers to increase the equilibrium offer. One way to accomplish this is to commit to have poor information via adopting a unanimity requirement. 2. By majority rule, we mean any threshold voting rule: that is, a proposal is accepted if the fraction voting to accept exceeds a pre-specified threshold. 3. The main exception is Coughlan (2000) , who shows that if pre-vote communication is possible and voter preferences are common knowledge and closely aligned, then both unanimity and majority rules may allow efficient aggregation of information. However, Austen-Smith and Feddersen (2006) show that if voter preferences are not common knowledge then unanimity is again the inferior voting rule from the perspective of information aggregation. Additionally, even Coughlan does not argue that unanimity rule is strictly superior to majority rule in the standard two-alternative voting game.
doi:10.1111/j.1467-937x.2009.00581.x fatcat:nfqohhfwyfgo5h6nxbkboh66ka