Essays on Mechanism Design and Positive Political Theory

. Essays on Mechanism Design and Positive Political Theory: Voting Rules and Behavior Dissertation Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Semin Kim, M.A. Graduate Program in Economics The Ohio State University 2014 Dissertation Committee: Yaron Azrieli, Advisor James Peck Katherine Baldiga Coffman . Copyright by Semin Kim 2014 . Abstract My dissertation focuses on the theory of mechanism design in voting environments, i.e., the design of voting rules that aggregate individual preferences into a group decision. The vast majority of the social choice literature on this topic uses purely ordinal models: agents can rank the candidates but the intensity of preferences is discarded. Furthermore, this literature restricts attention to dominant strategy rules- rules in which truth-telling is best for each agent regardless of other agents’ votes. My approach to the problem differs from the past literature in that, in my model, agents assign cardinal valuations to the alternatives, expressing their relative desirability. Instead of requiring dominant strategy, I consider the weaker concept of Incentive Compatibility (IC). IC only requires agents to be truth-telling if other agents do the same. My model is, therefore, close to the classic mechanism design problem, but with the crucial difference that monetary transfers cannot be used to remedy incentive problems. In Chapter 1, “Pareto efficiency and weighted majority rules” (joint with Yaron Azrieli), we study environments with two alternatives and independent private values, the simplest non-trivial environments. First, we show that the utilitarian rule subject to IC cannot utilize information about preference intensity, and that it is a weighted majority rule where the weights assigned to agents are environment-specific. Second, we characterize the set of Pareto efficient rules subject to IC and show that it is equal to the set of all weighted majority rules. We also study the stability of voting rules when a new rule is offered as an alternative to the incumbent. ii In Chapter 2, “Ordinal versus Cardinal Voting Rules: A Mechanism Design Ap- proach,” I consider neutral environments with at least three alternatives. Neutrality means that there is symmetry between the alternatives in the ex-ante stage, before preferences are realized. First, I show that within the class of ordinal rules (rules that do not use information about preference intensity) any Pareto efficient rule is incentive compatible. This result is quite interesting because unlike many of the classic results of mechanism design, it does not have tension between efficiency and incentive compatibility. Second, I construct a cardinal voting rule subject to IC, which achieves higher utilitarian social welfare than any ordinal rule. Thus, as opposed to environments with two alternatives, it is possible to increase social welfare by taking into account the intensity of preferences as reported by the agents when there are at least three alternatives. When there are exactly three alternatives my rule is closely related to Myerson’s (2002) (A,B) scoring rules, where each voter must choose a score vector that is a permutation of either (1,A,0) or (1,B,0). This is a simple rule that can practically be used in real-life institutions. iii . Dedication This work is dedicated to my parents and my wife, Hye Lin. Thanks for your love and support. iv . Acknowledgments I would like to express my special appreciation and thanks to my advisor, Yaron Azrieli. He has been a great mentor for me. I would like to thank him for encouraging my research and for his thoughtful guidance and comments. I would also like to thank my committee members, James Peck, Paul Healy, Katherine Baldiga Coffman for serving as my committee members and for their helpful comments and suggestions. A special thanks to my family and friends in my church. Words cannot express how grateful I am to them. Many thanks to Dan Levin, Caleb Cox, Daeyoung Jeong, Jack Rouzer, Robert Munk, Dimitry Mezhvinsky, Ian Krajbich, and seminar participants at The Ohio State University Theory and Experiments Group Meetings for their valuable comments. v . Vita 2009 . M.A. Economics, The Ohio State University 2009 to present . Graduate Teaching Associate, Department of Economics, The Ohio State University Fields of Study Major Field: Economics vi . Table of Contents Abstract . ii Dedication . iv Acknowledgments . v Vita.............................................................................vi List of Tables. .viii List of Figures . ix Chapter 1: Pareto Efficiency and Weighted Majority Rules . 1 Chapter 2: Ordinal versus Cardinal Voting Rules:A Mechanism Design Approach.40 Bibliography . 80 Appendix A: Proofs in Chapter 1 . 82 Appendix B: Proofs in Chapter 2 . 85 vii . List of Tables abc bac Table 1. Plurality and Borda count voting rules when v1 ∈ V1 and v1 ∈ V1 . .52 ∗ abcH 0 abcL Table 2. fB and f when v1 ∈ V1 and v1 ∈ V1 ..............................54 Table 3. The rule g in Example 3 . 74 Table 4. The rule g in Example 4 . 76 viii . List of Figures Figure 1. An example of discontinuous h (β) at βˆ ...............................66 ix CHAPTER 1 Pareto Efficiency and Weighted Majority Rules 1.1. Introduction Which mechanisms generate economically efficient outcomes when agents hold relevant private information? This is one of the most basic and important questions analyzed by the extensive mechanism design literature of the last several decades. In this paper we address this question in what is probably the simplest non-trivial environment: Society needs to choose between two alternatives, say reform or status- quo. Each agent is privately informed about his utility for each of the alternatives. The uncertainty of agents about the types of their opponents is captured by a common prior distribution, which we assume to be independent across agents. Monetary transfers are prohibited. The simplicity of the environment enables us to get a clear and precise answer to the above basic question, by characterizing the class of efficient mechanisms subject to incentive compatibility. The characterization depends on the particular notion of efficiency considered, but in all cases we find that the family of weighted majority rules plays an important role. These voting mechanisms, which include the simple majority rule as a special case, are widely used in practice and have been extensively studied in the political and economic literature.1 We think of our results as providing a normative rationale for the use of weighted majority rules, one that is based on the classic notions of efficiency and incentive compatibility. 1See the related literature section below for references. 1 Let us be more explicit regarding what we call a weighted majority rule. A Social Choice Function (SCF) f is a mapping from type profiles to lotteries over {reform, status-quo}. We say that f is a weighted majority rule if we can find positive weights (w1, . , wn) for the agents and a positive quota q, such that under f the reform is implemented if the sum of weights of agents that prefer the reform exceeds q, and the status-quo prevails if this sum is less than q. Ties are allowed to be broken in an arbitrary way. Our first result (Theorem 1) characterizes SCFs that maximize (ex-ante, utilitarian) social welfare subject to incentive compatibility.2 We show that a SCF is a solution to this optimization problem if and only if it is a weighted majority rule with specific weights. In particular, incentive compatibility constraints prevent effec- tive use of any information about realized intensity of preferences; only the ordinal ranking of the two alternatives as reported by the agents matters for the outcome. However, the distribution of intensities is relevant for determining the optimal rule, since, roughly speaking, the weight assigned to agent i in the optimal rule reflects the expected utility gain of i if his favorite alternative is chosen. We then move on to characterize the classes of interim and ex-ante incentive efficient SCFs (Theorems 2 and 3). First, we show that a SCF is interim incentive efficient if and only if it is a weighted majority rule. In other words, the Pareto frontier (in the interim stage) of the set of incentive compatible decision rules coin- cides with the class of weighted majority rules. Second, we characterize the subset of weighted majority rules which are also ex-ante incentive efficient by imposing re- strictions on their weights and quota. Thus, in environments that are likely to satisfy our assumptions, the only kind of decision schemes that should be used are weighted 2By the revelation principle, and assuming that agents play Bayes-Nash equilibrium, incentive compatibility constraints exactly characterize the class of feasible SCFs. 2 majority rules. Indeed, any other incentive compatible rule is Pareto inferior to some (incentive compatible) weighted majority rule. These results are proved by showing that a SCF is (interim or ex-ante) incentive efficient in a given environment if and only if it is a maximizer of social welfare in an auxiliary “equivalent” environment, and then applying Theorem 1. While the environment we analyze is simple, we emphasize that no symmetry between the agents or the alternatives is assumed. Even at the ex-ante stage, different agents may have different utility distributions, and these distributions may be biased in favor of one of the alternatives. We believe that this is an important feature of our analysis, since many real-life environments are inherently asymmetric. Examples include representative democracies with heterogenous district sizes, publicly held firms with institutional and private shareholders, and faculty hiring decisions in which the job candidate has closer research interests to some faculty members than others. We discuss the implications of our results for some of these environments in Section 1.8.

Load more