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

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 $${align*} pₜ( a,A) ={eu( a) /λ( t) +α( a)}{∑b∈ Aeu( b) /λ( t) +α( b)}, {align*}$$ where $pₜ( a,A)$ 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).