List-rationalizable choice

A choice function is \textit{list rational(izable)}, if there is a fixed \textit{list} such that for each \textit{choice set}, successive comparison of the alternatives by following the \textit{list} retrieves the chosen alternative. We extend the formulation of list rationality to stochastic choice setup. We say two alternatives are related if the \textit{stochastic path independence condition} is violated between these alternatives. We show that a random choice function is list rational if and only if this relation is acyclic. Our characterization for deterministic choice functions follows as a corollary. By using this characterization, we relate list rationality to two-stage choice procedures.