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

Abstract

We provide two characterizations, one axiomatic and the other neuro-computational, of the dependence of choice probabilities on deadlines, within the widely used softmax representation p t ( a , A ) = e u ( a ) λ ( t ) + α ( a ) ∑ b ∈ A e u ( b ) λ ( t ) + α ( b ) , where p t ( a , A ) is the probability that alternative a is selected from the set A of feasible alternatives if t is the time available to decide, λ is a time-dependent noise parameter measuring the unit cost of information, u is a time-independent utility function, and α is an alternative-specific bias that determines the initial choice probabilities (reflecting prior information and memory anchoring). Our axiomatic analysis provides a behavioural foundation of softmax (also known as Multinomial Logit Model when α is constant). Our neuro-computational derivation provides a biologically inspired algorithm that may explain the emergence of softmax in choice behaviour. Jointly, the two approaches provide a thorough understanding of softmaximization in terms of internal causes (neuro-physiological mechanisms) and external effects (testable implications).