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.
The research successfully proved existence of equilibrium and characterized its properties for environments with multiple issues and private values. The characterizations suggest the possibility of extreme inefficiencies for elections that simultaneously decide multiple issues. These findings were published in "Combinatorial Voting" in Econometrica. The research also established and equivalence between separate and unified large elections for environments with multiple issues and common values. These findings were published in "The Condorcet Jur(ies) Theorem" in the Journal of Economic Theory. The PI's also collected experimental data to confirm the predictions of the models. The analysis of these data is still ongoing, but preliminary tests suggests a surprising corroboration of the sophisticated behaviors predicted in the models. Intellectually, the research contributed to the emerging theoretical study of elections with more than two outcomes. This research examined the special case where the outcomes have a combinatorial structure, that is naturally induced by having multiple binary outcomes that are simultaneously decided. Together, the findings suggest that policy and intentional design of ballots has an important role in situations where there are divergent interests and preferences need to be aggregated. On the other hand, they also suggest that the role of design, for example whether to combine or separate defendants being tried for similar crimes, is less important in situations where information is aggregated.
