Multinomial logit processes and preference discovery: outside and inside the black box
Fabio Maccheroni and
No 663, Working Papers from IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University
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, 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, is a time dependent noise parameter measuring the unit cost of information, u is a time independent utility function, and is an alternative-specific bias that determines the initial choice probabilities and possibly reáects prior information. Our axiomatic analysis provides a behavioral foundation of softmax (also known as Multinomial Logit Model when 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 e§ects (testable implications). Keywords: Discrete Choice Analysis, Drift Di§usion Model, Heteroscedastic Extreme Value Models, Luce Model, Metropolis Algorithm, Multinomial Logit Model, Quantal Response Equilib ium, Rational Inattention
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