A characterization of the Luce choice rule for an arbitrary collection of menus

Abstract

The Luce Choice Rule (or, equivalently, the multinomial logit model) is extensively used in economics and other fields. Classical characterizations rest on Luce's Choice Axiom, when all choice sets are available, and Luce's Product Rule in the case of binary choice. Yet, actual datasets typically consist neither of all choice sets nor all binary choice sets. We provide a characterization for the general case, allowing also for zero choice probabilities. Building upon this characterization, we derive implications for experimental design in terms of three criteria: falsification, identification, and prediction.