The lexicographic method in preference theory

Abstract

Lexicographically ordered sets of binary criteria provide a uniform measure of how concisely a preference can be represented and how efficiently an agent can make decisions. This measure leads to: (1) sharper 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. Lexicographically ordered binary criteria can also generate preferences that strictly order every pair of bundles in Rn and have utility representations, thus reconciling utility theory with behavioral theories that rule out indifference. Finally, the lexicographic method provides simple proofs that transitive orders can be extended to linear orders.