Multinomial logit processes and preference discovery: inside and outside the black box

2020/04/28 by Cerreia-Vioglio, Simone, Maccheroni, Fabio, Marinacci, Massimo +1
#FOS: Biological sciences #FOS: Economics and business #Neurons and Cognition (q-bio.NC) #Theoretical Economics (econ.TH)

paper · doi:10.48550/arxiv.2004.13376

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) =\dfrace^{(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 behavioral 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 behavior. Jointly, the two approaches provide a thorough understanding of soft-maximization in terms of internal causes (neurophysiological mechanisms) and external effects (testable implications).

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