Essays in Economic Theory

Abstract

This thesis consists of five chapters on topics in mechanism design and voting.<br /> In Chapter 1, we study a committee deciding collectively whether to accept a given proposal or to maintain the status quo. Committee members are privately informed about their valuations and monetary transfers are possible. According to which rule should the committee make its decision? We consider strategy-proof and anonymous social choice functions and solve for the decision rule that maximizes utilitarian welfare, which takes monetary transfers to an external agency explicitly into account. For regular distributions of preferences, we find that it is optimal to exclude monetary transfers and to decide by qualified majority voting. This sheds new light on the common objection that criticizes voting for its inefficiency.<br /> In Chapter 2, we study welfare-optimal decision rules for committees that repeatedly take a binary decision. Committee members are privately informed about their payoffs and monetary transfers are not feasible. In static environments, the only strategy-proof mechanisms are voting rules which are inefficient as they do not condition on preference intensities. The dynamic structure of repeated decision-making allows for richer decision rules that overcome this inefficiency. Nonetheless, we show that often simple voting is optimal for two-person committees. This holds for many prior type distributions and irrespective of the agents' patience.<br /> In Chapter 3, we study binary, sequential voting procedures in settings with privately informed agents and single-peaked (or single-crossing) preferences. We identify two conditions on binary voting trees, convexity of divisions and monotonicity of qualified majorities, ensuring that sincere voting at each stage forms an ex-post perfect equilibrium in the associated extensive form game with incomplete information. We illustrate our findings with several case studies: procedures that do not satisfy our two conditions offer ample space for strategic manipulations. Conversely, when the agenda satisfied our conditions, sincere behavior was indeed the most likely outcome.<br /> In Chapter 4, we study how a principal should optimally choose between implementing a new policy and keeping status quo when the information relevant for the decision is privately held by agents. Agents are strategic in revealing their information, but the principal can verify an agent's information at a given cost. We exclude monetary transfers. When is it worthwhile for the principal to incur the cost and learn an agent's information? We characterize the mechanism that maximizes the expected utility of the principal. This mechanism can be implemented as a weighted majority voting rule, where agents are given additional weight if they provide evidence about their information. The evidence is verified whenever it is decisive for the principal's decision. Additionally, we find a general equivalence between Bayesian and ex-post incentive compatible mechanisms in this setting.<br /> In Chapter 5, we are interested in strategy-proof mechanisms that maximize the agents' residual surplus, that is, the utility derived from the physical allocation minus transfers accruing to an external entity, in an independent private value auction environment. We find that, under the assumption of an increasing hazard rate of type distributions, an optimal deterministic mechanism never extracts any net payments from the agents, that is, it will be budget-balanced. Specifically, optimal mechanisms have a simple "posted price'' or "option'' form. In the bilateral trade environment, we obtain optimality of posted price mechanisms without any assumption on type distributions.