Essays in Individual and Collective Choice

Abstract

This thesis consists of three chapters that address problems in social choice theory, fair division of a heterogeneous good and choosing a pair of complementary goods, respectively. The first chapter deals with designing a voting mechanism. There are a set of finite alternatives arranged according to an exogenous order. The output of the mechanism must be a (fixed-cardinality) set of contiguous alternatives, that are referred to as intervals. We find a mechanism that is Pareto efficient and strategy-proof. In the second chapter we study the division of a heterogeneous resource. Each agent must be allocated a continuous (interval) subset of the interval [0,1]. The agents have preferences that are single-peaked in one dimension (quantity) but not in another (location). We characterize the full set of Pareto efficient and envy-free (i.e. fair) allocations. We also show that there is no rule that is strategy-proof, envy-free and Pareto efficient. In the third chapter we propose a heuristic on how a decision-maker (DM) might choose a pair of complementary goods, one alternative each from two sets. The modeling of complementarity is done without relying on prices or utility functions. The choices of the DM are represented by joint choice functions. We first define the concepts of weak and strong-complements. Further we characterize what we call weak-complements choice functions and then provide necessary and sufficient conditions for the existence of strong-complements choice functions.