Deciding who, what, why, and how : aggregating preferences over agents, alternatives, axioms, and rules

Abstract

Collective decision making requires dealing with competing preferences. One probably needs little convincing that such problems can be complex and difficult to solve. There are many types of preferences, many different ways of expressing them, many different spaces of possible outcomes, and many different objectives to consider. While there is no universal preference aggregation mechanism that is applicable to all problems, preference aggregation mechanisms can be designed using reasonable models of agent preferences and behavior and sensible measures of performance for specific classes of problems. This dissertation is organized into three parts. Part I uses economic utility to describe agents' preferences and to define objectives. The challenge here is that agents are only able to present limited information about their preferences. Part I focuses on centralized algorithms that take in agent preferences and produce an outcome that is provably close to optimal when there is not sufficient information available to compute the optimal outcome. The objective here is to maximize the sum of agent utilities or minimize the sum of agent costs. % Chapter 4 looks at a class of problems where agents have preferences over one another, while Chapter 5 looks at agent preferences over inert alternatives. Part II moves away from utilitarian reasoning and considers the interplay between the two types of preference objects introduced earlier -- agents and inert alternatives. Chapter 7 has agents who each must be assigned, or assign themselves, to a single alternative. The agents have preferences based upon both the alternative to which they are assigned and how many other agents are assigned to it. The central consideration of Chapter 7 is what outcomes are stable in the sense that agents cannot deviate profitably to yield an outcome they prefer. Chapter 8 has agents using elections and a method of proxy voting to empower other agents as representatives to make decisions on their behalf. Following Chapter 5, agents' preferences over potential representatives are based on the distance between them according to a certain metric and the goal is to approximate an optimal outcome. While in Chapter 5 an arbitrary metric is considered, Chapter 8 uses an explicit metric, and while the goal in Chapter 5 is to minimize the sum of agent costs, the goal in Chapter 8 is to achieve using indirect methods the same outcome that would be selected if all the agents voted directly without representatives. Whereas the agents throughout Parts I-II only have preferences over inert alternatives, agents, or a combination of the two, the agents in Part III have a new type of preference object. In Part III agents share the concerns that any mechanism designer might. The agents now care how collective decisions are made, not only about the outcome. % Chapter 10 demonstrates that when agents agree on how decisions should be made, they can construct a set of self-regulating rules, or a constitution capable of amending itself. Lastly, Chapter 11 extends the traditional models of Social Choice to reveal that even when agents disagree on how decisions should be made rational collective choices are possible.