Combinatorial Voting

University Of California-Berkeley, Berkeley CA

Investigators

Abstract

Many elections decide multiple issues simultaneously with a single ballot. The desirability of certain issues depends on how others are resolved: a typical California ballot includes spending initiatives, bond measures, and tax propositions which jointly impact the fiscal positions of state and local governments. With such nonseparabilities, strategic voting over multiple issues introduces subtle considerations absent from single-issue elections. For example, a voter might support a school bond measure only if a proposition to increase the sales tax is also approved to mitigate the fiscal burden of financing the bond. Then, in deciding her vote on the bond measure, she should consider the probability of the complementary tax increase being approved. Moreover, since her vote on the bond measure matters only if she is pivotal, she should condition the likelihood of the tax increase under the assumption that the other voters have split equally on the bond measure. This project commences the equilibrium analysis of elections with interdependent issues. Existing models of strategic voting either consider a single issue or assume that preferences are separable across issues. For the more general environments considered in this proposal, the following fundamental questions regarding strategic voting are yet unresolved: Does a voting equilibrium exist? How is this equilibrium characterized? How does it behave as the electorate becomes large? How efficient is this equilibrium? The researchers study these questions in a voting environment with uncertainty, modeled as a Bayesian game. The project seeks to compare the expected efficiency of different mechanisms for these environments. For example, voting sequentially over issues one at a time progressively resolves uncertainty and may improve expected welfare. Second, the project aims to understand interdependent values and information aggregation with multiple issues. In particular, if each voter receives a noisy signal regarding the common values of different combinations, will the most desired bundle pass almost surely as the electorate (hence the amount of information) becomes large? Broader impacts. Twenty-four American states and numerous localities use referenda to decide an array of propositions, ranging from property taxes to affirmative action. Any progress towards institutional improvements in referenda could yield large social benefits. The popularization of direct democracy presents voters with an ever-increasing number of issues, along with the accompanying multiplication in the number of potential interdependencies. This project seeks to understand the strategic effects of nonseparabilities on voting, and their consequent impact on outcomes and welfare.