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 \[ p_{t}\left( a,A\right) =e^{\frac{u\left( a\right) {\lambda \left( t\right) }+\alpha \left( a\right) }}{b\in Ae^{u\left( b\right) {\lambda \left( t\right) }+\alpha \left( b\right) }}\% \] where p_{t}\left( a,A\right) 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 and possibly reflects prior information . 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).
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 \[ p_{t}\left( a,A\right) =e^{\frac{u\left( a\right) {\lambda \left( t\right) }+\alpha \left( a\right) }}{b\in Ae^{u\left( b\right) {\lambda \left( t\right) }+\alpha \left( b\right) }}\% \] where p_{t}\left( a,A\right) 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).
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and possibly reflects prior information
reflecting prior information and memory anchoring