Multinomial Logit Processes and Preference Discovery: Outside and Inside the Black Box

Abstract

We provide two characterizations, one axiomatic and the other neuro-computational, of the dependence of choice probabilities on deadlines in the softmax form, with time independent utility function, time dependent noise parameter, that measures the unit cost of information, and alternative-specific bias, that determines the initial choice probabilities reflecting prior information and memory anchoring.

Our axiomatic analysis provides a behavioral foundation of softmax (also known as Multinomial Logit Model when bias is absent). Our neuro-computational derivation provides a biologically inspired algorithm that may explain the emergence of softmax in choice behavior. Jointly, the two approaches provide a thorough understanding of soft-maximization in terms of internal causes (neurophysiological mechanisms) and external effects (testable implications).

Keywords: Discrete Choice Analysis, Drift Diffusion Model, Heteroscedastic Extreme Value Models, Luce Model, Metropolis Algorithm, Multinomial Logit Model, Quantal Response Equilibrium, Rational Inattention

JEL Classification: D81, D87