Essays in Collective Decision-Making

Abstract

Group decisions are ubiquitous in democratic societies. They range from general elections, and referenda to voting inside various organizations such as political institutions, and corporate boards. The present dissertation consists of four self-contained essays that study the design of voting mechanisms in settings with multiple alternatives. The normative essays identify reasonable voting rules for different contexts. Methodologically, the analyses are theoretical, and mathematical. They build upon tools from microeconomic theory, and, in particular, game theory, and mechanism design. <br /> The "one person, one vote" criterion is a principle that is central to democracy, but it is arguably with justification violated in certain situations, where the voters are asymmetric. Chapters 1 and 2 share the following overarching research question: How to assign voting weights to heterogeneous agents? <br /> Chapter 1, Sequential Voting and the Weights of Nations, focuses on institutions of representative democracy such as the Council of the European Union, where representatives vote on behalf of groups of citizens of heterogeneous size. The chapter develops a model of representative democracy, and studies the design of welfare-maximizing voting mechanisms for the collective decision-making process involving representatives. <br /> Chapter 2, Public Goods Provision and Weighted Majority Voting, considers the problem of optimally providing public goods, that is, non-excludable, and non-rivalrous goods. It analyzes the utilitarian voting mechanism for the provision of a costly public good. The voters are asymmetric in the following two ways: On the one hand, the asymmetry of the voters arises from heterogeneous distributions of the benefits of the public good. On the other hand, voters are asymmetric because of an unequal sharing of the costs of the public good. <br /> Chapter 3, Committee Search Design, is joint work with Christina Luxen. Search processes in many organizations such as hiring procedures share the following two characteristics: The decisions are taken collectively by a committee via voting, and the committee evaluates multiple items simultaneously. The present chapter investigates sequential search by committee, where, in each period of time, K items can be sampled, and at least M out of N committee members have to approve an item in order to stop search. The focus of the chapter is on the design of the sample size per period, K. <br /> Chapter 4, Optimal Voting Mechanisms on Generalized Single-Peaked Domains, examines welfare-maximizing voting mechanisms in settings, where the voters have generalized single-peaked preferences derived from median spaces as introduced in Nehring and Puppe (2007). These preference structures are considerably larger than the class of single-peaked preferences on a line. The general optimality result in the chapter is applied to the design of voting mechanisms for the provision of two costly public goods subject to the constraint that the provided level of the former good is weakly higher than the provided level of the latter good.