Date of Award
8-2002
Degree Name
Doctor of Philosophy
Department
Mathematics
Abstract
Whenever a decision-maker must express simultaneously his or her preferences on several possibly related issues, the existence of interdependence among these preferences can lead to collective decisions that are unsatisfactory or even paradoxical. Intuitively, an individual’s preferences are said to be separable on a subset of issues if they do not depend on the choice of alternatives for issues outside the subset. Here we explore from a mathematical standpoint the properties of separable and nonseparable preference orders. We begin by formulating a general model of multidimensional preferences and we formally introduce the notions of separability and noninfluentiality. We study the structure of interdependent preferences and explore connections to the previous notions of separability studied in economics. Next, we examine some of the properties and constructions related to separability. We consider lexicographic and additive orders and use simple tools from set theory to study k-majority aggregation of separable preferences. We show that, in contrast to famous results such as Condorcet’s Voting Paradox, the property of separability is preserved by this natural aggregation scheme. We address the problem of enumerating separable preference orders and introduce the notions of monoseparable, symmetric, preseparable and strongly preseparable preferences. Counting formulas are developed for the latter three of these classes. Finally, we consider the action of the symmetric group on the set of binary preference orders. We characterize the group of symmetry-preserving permutations and the group of separability-preserving permutations, providing useful insights into the extreme sensitivity to small changes exhibited by separable preferences.
Access Setting
Dissertation-Open Access
Recommended Citation
Hodge, Jonathan K., "Separable Preference Orders" (2002). Dissertations. 1282.
https://scholarworks.wmich.edu/dissertations/1282