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We provide two characterizations, one axiomatic and the otherneuro-computational, of the dependence of choice probabilities on deadlines,within the widely used softmax representation \[ p_{t}\left( a,A\right)=\dfrac{e^{\frac{u\left( a\right) }{\lambda \left( t\right) }+\alpha \left(a\right) }}{\sum_{b\in A}e^{\frac{u\left( b\right) }{\lambda \left( t\right)}+\alpha \left( b\right) }}% \] where $p_{t}\left( a,A\right) $ is theprobability that alternative $a$ is selected from the set $A$ of feasiblealternatives if $t$ is the time available to decide, $\lambda$ is a timedependent noise parameter measuring the unit cost of information, $u$ is a timeindependent utility function, and $\alpha$ is an alternative-specific bias thatdetermines the initial choice probabilities reflecting prior information andmemory anchoring.  Our axiomatic analysis provides a behavioral foundation of softmax (alsoknown as Multinomial Logit Model when $\alpha$ is constant). Ourneuro-computational derivation provides a biologically inspired algorithm thatmay explain the emergence of softmax in choice behavior. Jointly, the twoapproaches provide a thorough understanding of soft-maximization in terms ofinternal causes (neurophysiological mechanisms) and external effects (testableimplications).

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