The Lexicographic Method in Preference Theory

Abstract

Choosing among alternatives by proceeding lexicographically through a sequence of criteria can serve as a theoretical tool as well as a practical way to make decisions. First, sequences of criteria can generate monotone preferences that satisfy a fractal or self-similarity property, strictly rank every pair of bundles in ℝⁿ, and have utility representations. Second, sequences of binary criteria provide a uniform measure of how concisely a preference can be represented. This measure leads to: (1) more plausible conclusions about which preferences are easy to represent than the economics test of checking if a preference has a utility representation, (2) a generalization of the classical result that a preference has a utility representation if and only if it has a countable order-dense subset. Finally we provide simple proofs of the extension theorems that show that strict partial orders can be extended to linear orders.

Keywords: lexicographic utility, fractals, preference representation, Szpilrajn's Theorem

JEL Classification: D11, C65