Essays in Social Choice and Econometrics

Abstract

The dissertation studies the property of transitivity in the social choice theory. I explain why we should care about transitivity in decision theory. I propose two social decision theories: redistribution regret and ranking regret, study their properties of transitivity, and discuss the possibility to find a best choice for the social planner. Additionally, in the joint work, we propose a general method to construct a consistent estimator given two parametric models, one of which could be incorrectly specified. In “Why Transitivity”, to explain behaviors violating transitivity, e.g., preference reversals, some models, like regret theory, salience theory were developed. However, these models naturally violate transitivity, which may not lead to a best choice for the decision maker. This paper discusses the consequences and the possible extensions to deal with it. In “Redistribution Regret and Transitivity”, a social planner wants to allocate resources, e.g., the government allocates fiscal revenue or parents distribute toys to children. The social planner cares about individuals' feelings, which depend both on their assigned resources, and on the alternatives they might have been assigned. As a result, there could be intransitive cycles. This paper shows that the preference orders are generally non-transitive but there are two exceptions: fixed total resource and one extremely sensitive individual, or only two individuals with the same non-linear individual regret function. In “Ranking Regret”, a social planner wants to rank people, e.g., assign airline passengers a boarding order. A natural ranking is to order people from most to least sensitive to their rank. But people's feelings can depend both on their assigned rank, and on the alternatives they might have been assigned. As a result, there may be no best ranking, due to intransitive cycles. This paper shows how to tell when a best ranking exists, and that when it exists, it is indeed the natural ranking. When this best does not exist, an alternative second-best group ranking strategy is proposed, which resembles actual airline boarding policies. In “Over-Identified Doubly Robust Identification and Estimation”, joint with Arthur Lewbel and Jinyoung Choi, we consider two parametric models. At least one is correctly specified, but we don't know which. Both models include a common vector of parameters. An estimator for this common parameter vector is called Doubly Robust (DR) if it's consistent no matter which model is correct. We provide a general technique for constructing DR estimators (assuming the models are over identified). Our Over-identified Doubly Robust (ODR) technique is a simple extension of the Generalized Method of Moments. We illustrate our ODR with a variety of models. Our empirical application is instrumental variables estimation, where either one of two instrument vectors might be invalid.