Approximate Judgement Aggregation

In this paper we analyze judgement aggregation problems in which a group of agents independently votes on a set of complex propositions that has some interdependency constraint between them (e.g., transitivity when describing preferences). We consider the issue of judgement aggregation from the perspective of approximation. That is, we generalize the previous results by studying approximate judgement aggregation. We relax the main two constraints assumed in the current literature, Consistency and Independence and consider mechanisms that only approximately satisfy these constraints, that is, satisfy them up to a small portion of the inputs. The main question we raise is whether the relaxation of these notions significantly alters the class of satisfying aggregation mechanisms. The recent works for preference aggregation of Kalai, Mossel, and Keller fit into this framework. The main result of this paper is that, as in the case of preference aggregation, in the case of a subclass of a natural class of aggregation problems termed `truth-functional agendas', the set of satisfying aggregation mechanisms does not extend non-trivially when relaxing the constraints. Our proof techniques involve Boolean Fourier transform and analysis of voter influences for voting protocols. The question we raise for Approximate Aggregation can be stated in terms of Property Testing. For instance, as a corollary from our result we get a generalization of the classic result for property testing of linearity of Boolean functions.judgement aggregation, truth-functional agendas, computational social choice, computational judgement aggregation, approximate aggregation, inconsistency index, dependency index

Social Choice for Partial Preferences Using Imputation

Within the field of multiagent systems, the area of computational social choice considers the problems arising when decisions must be made collectively by a group of agents. Usually such systems collect a ranking of the alternatives from each member of the group in turn, and aggregate these individual rankings to arrive at a collective decision. However, when there are many alternatives to consider, individual agents may be unwilling, or unable, to rank all of them, leading to decisions that must be made on the basis of incomplete information. While earlier approaches attempt to work with the provided rankings by making assumptions about the nature of the missing information, this can lead to undesirable outcomes when the assumptions do not hold, and is ill-suited to certain problem domains. In this thesis, we propose a new approach that uses machine learning algorithms (both conventional and purpose-built) to generate plausible completions of each agent’s rankings on the basis of the partial rankings the agent provided (imputations), in a way that reflects the agents’ true preferences. We show that the combination of existing social choice functions with certain classes of imputation algorithms, which forms the core of our proposed solution, is equivalent to a form of social choice. Our system then undergoes an extensive empirical validation under 40 different test conditions, involving more than 50,000 group decision problems generated from real-world electoral data, and is found to outperform existing competitors significantly, leading to better group decisions overall. Detailed empirical findings are also used to characterize the behaviour of the system, and illustrate the circumstances in which it is most advantageous. A general testbed for comparing solutions using real-world and artificial data (Prefmine) is then described, in conjunction with results that justify its design decisions. We move on to propose a new machine learning algorithm intended specifically to learn and impute the preferences of agents, and validate its effectiveness. This Markov-Tree approach is demonstrated to be superior to imputation using conventional machine learning, and has a simple interpretation that characterizes the problems on which it will perform well. Later chapters contain an axiomatic validation of both of our new approaches, as well as techniques for mitigating their manipulability. The thesis concludes with a discussion of the applicability of its contributions, both for multiagent systems and for settings involving human elections. In all, we reveal an interesting connection between machine learning and computational social choice, and introduce a testbed which facilitates future research efforts on computational social choice for partial preferences, by allowing empirical comparisons between competing approaches to be conducted easily, accurately, and quickly. Perhaps most importantly, we offer an important and effective new direction for enabling group decision making when preferences are not completely specified, using imputation methods

Public Institutions and Private Incentives: Three Essays

No abstract available

Essays in Economic Theory

This thesis studies information aggregation and reputation management in three microeconomic environments. In the first chapter, I consider a committee voting setup with two rounds of voting where committee members who possess private information about the state of the world have to make a binary decision. I investigate incentives for truthful revelation of their information in the first voting period. Coughlan (2000) shows that members reveal their information in a straw poll only if their preferences are homogeneous. By taking costs of time into account, I demonstrate that committees have strictly higher incentives to reveal information if a decision with high levels of consensus can already be made in the straw poll. In such scenarios, members of all homogeneous and some heterogeneous juries are strictly better off when the requirement for early decisions is chosen carefully. The second chapter studies a seller whose reputation is determined by the types of her customers. In the model, a monopolist repeatedly sells a good to heterogeneous customers who, depending on their type, increase or decrease the seller's reputation. First, I study a trade-off between realizing current-period profits and building reputation for future periods. Second, I analyze reputation dynamics. Over time, reputation always converges to a stable level. Convergence behavior, however, depends strongly on the good's durability. While the reputation of less durable goods fluctuates around the long-run reputation, the reputation of more durable goods converges monotonically. In the third chapter, I examine a dynamic reputation model in which a long-lived online seller of unknown logistical ability competes against an offline retailer. In order to deliver goods to her short-lived buyers, the online seller has to employ one of two shippers which differ in their expected delivery time. Her buyers, in turn, update their beliefs about the seller's logistical ability based on their experienced waiting time for the good. I find that incentives to assign a fast shipper depend significantly on the information about the delivery process that buyers can observe. I compare the equilibrium outcomes of four specifications where buyers can or cannot observe the shipper's quality upon delivery of the good, and can or cannot track and trace the delivery process in detail. The ability to track the delivery proves harmful to the buyers' welfare in most cases, whereas the ability to observe the shipper's quality can be beneficial or harmful depending on the exact setup and parameter specification

Opinion Dynamics and Learning in Social Networks

We provide an overview of recent research on belief and opinion dynamics in social networks. We discuss both Bayesian and non-Bayesian models of social learning and focus on the implications of the form of learning (e.g., Bayesian vs. non-Bayesian), the sources of information (e.g., observation vs. communication), and the structure of social networks in which individuals are situated on three key questions: (1) whether social learning will lead to consensus, i.e., to agreement among individuals starting with different views; (2) whether social learning will effectively aggregate dispersed information and thus weed out incorrect beliefs; (3) whether media sources, prominent agents, politicians and the state will be able to manipulate beliefs and spread misinformation in a society