An Optimal Voting System When Voting is Costly - A Case Study in Dynamic Mechanism Design

We propose a formulation for the problem of designing an optimal dynamic voting system when voting is costly. The possibility to coordinate participation by voting sequentially requires explicit maximization over a set of dynamic mechanisms which involves some arguments that are new to the theory of mechanism design. For a highly stylized specification of our model with private values and two alternatives we show the optimality of a voting system that combines two main elements: (i) there is an arbitrarily chosen default decision and non-participation is interpreted as a vote in favor of the default; (ii) voting is sequential and is terminated when a supermajority requirement, which declines over time, is met. We show the optimality of such a voting system by arguing that it is first best, that is, it maximizes welfare when incentive compatibility constraints are ignored, and by showing that individual incentives and social welfare can be sufficiently aligned to make a first best system incentive compatible. This paper supersedes a previous draft entitled "Dynamic Mechanism Design with Costly Participation." We are grateful to Arthur Lupia, Romans Pancs, Alessandro Pavan, Marek Pycia, Ilya Segal, Ricky Vohra, and two anonymous referees for helpful comments and to Yan-Min Choo for research assistance. Tilman Börgers thanks the Center for Mathematical Studies in Economics and Management Science at Northwestern University for the hospitality that it offered while he was working on this paper. Moritz Meyer-ter-Vehn thanks the Hausdorff Research Institute for Mathematics in Bonn for its hospitality, which he enjoyed while working on this paper. [email protected]. Department of Economics, University of Michigan, [email protected]. Department of Economics, UCLA, [email protected].