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 [ p_{t}left( a,Aright) =dfrac{e^{frac{uleft( aright) }{lambda left( tright) }+alpha left( aright) }}{sum_{bin A}e^{frac{uleft( bright) }{lambda left( tright) }+alpha left( bright) }}% ] where $p_{t}left( a,Aright) $ is the probability that alternative $a$ is selected from the set $A$ of feasible alternatives if $t$ is the time available to decide, $lambda$ is a time dependent noise parameter measuring the unit cost of information, $u$ is a time independent utility function, and $alpha$ is an 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 $alpha$ is constant). 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).