no code implementations • 17 Jul 2020 • Simone Cerreia-Vioglio, Per Olov Lindberg, Fabio Maccheroni, Massimo Marinacci, Aldo Rustichini
We prove that a random choice rule satisfies Luce's Choice Axiom if and only if its support is a choice correspondence that satisfies the Weak Axiom of Revealed Preference, thus it consists of alternatives that are optimal according to some preference, and random choice then occurs according to a tie breaking among such alternatives that satisfies Renyi's Conditioning Axiom.
no code implementations • 28 Apr 2020 • Simone Cerreia-Vioglio, Fabio Maccheroni, Massimo Marinacci, Aldo Rustichini
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 \[ p_{t}\left( a, A\right) =\dfrac{e^{\frac{u\left( a\right) }{\lambda \left( t\right) }+\alpha \left( a\right) }}{\sum_{b\in A}e^{\frac{u\left( b\right) }{\lambda \left( t\right) }+\alpha \left( b\right) }}% \] where $p_{t}\left( a, A\right) $ is 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.
