Bray Theory Workshop

We study elections that simultaneously decide multiple issues, where voters have independent private values over bundles of issues. The innovation is considering nonseparable preferences, where issues may be complements or substitutes. Voters face a political exposure problem: the optimal vote for a particular issue will depend on the resolution of the other issues. Moreover, the probability that another issue will pass should be conditioned on being pivotal. We prove equilibrium exists when distributions over values have full support or when issues are complements. We study limits of symmetric equilibria for large elections. Suppose that, conditioning on being pivotal for an issue, the outcomes of the residual issues are asymptotically certain. Then limit equilibria are determined by ordinal comparisons of bundles. We characterize when conditional certainty occurs. Using these characterizations, we construct an nonempty open set of distributions where all limit equilibria maintain uncertainty regarding the outcome of the election. Thus, predictability of large elections is not a generic feature of independent private values. We examine the ordinal efficiency of limit equilibria. While the outcome can be unpredictable even without the existence of a Condorcet cycle, we provide sufficient conditions on the type distribution which guarantee predictability.