Essays on resource allocation and social choice

Thesis (Ph. D.)--University of Rochester. Dept. of Economics, 2012.This thesis is a collection of essays on resource allocation and social choice problems. In Chapters 1 and 2, we study the problem of assigning a set of objects to a set of agents. We allow no monetary transfers and focus on probabilistic methods. The serial rule (Bogomolnaia and Moulin, 2001) occupies a central place in this literature, as a rule satisfying stochastic-dominance-efficiency (the notation "sd" stands for "stochastic-dominance" below) and sd-no-envy. However, until recently, its axiomatic characterization has been elusive. In Chapter 1, we assume that each agent has preferences over objects with no indifference. We also accommodate the possibility that each agent may consume more than one object. We generalize the serial rule to be applicable to this setting. Our main result is a characterization of this rule by means of sd-efficiency, sd-normalized no-envy, limited invariance, and consistency. This result persists if we replace sd-normalized-no-envy by the sd-proportional division lower bound, and consistency by converse consistency, or both. In Chapter 2, we allow indifference among objects. Katta and Sethuraman (2006) propose the extended serial correspondence as an adaptation of the serial rule. Our first result is a characterization of the extended serial correspondence in welfare terms by means of sd-efficiency, sd-no-envy, and bounded invariance which we adapt from Bogomolnaia and Heo (2012). Next, we introduce a restriction on preference profiles. We show that for each profile with "full support on partition," an assignment matrix is sd-efficient and sd-envy-free if and only if it is selected by the extended serial correspondence.< In Chapter 3, we study the problem of selecting the locations of two identical public facilities on an interval. Each agent has a single-peaked ranking over single locations and uses only one facility, the one he prefers. We introduce a class of rules, which we call double median rules. Our first result is its characterization by means of continuity with respect to preferences, anonymity, strategy-proofness, and users only. We next identify the subclasses of these rules satisfying additional requirements. We also discuss the class of multiple median rules for more than two public facilities