Rational choice with full-comparability domains

We propose a new model of choice in the presence of incomplete preferences. Instead of simply choosing an element which is maximal according to her preferences, the decision maker divides the space of alternatives into subdomains inside which her preferences are complete. She then maximizes her preferences inside these domains of full comparability. Representation theorems are given in which the decision maker always satisfies a weaker form of the Weak Axiom of Revealed Preference and different postulates are imposed on a general notion of revealed preference. They identify a class of choice correspondences that is nested between choice correspondences represented by multiple rationales and the standard model of rational choice. In addition, we suggest that our results provide a useful tool to adapt models that were otherwise restricted to deterministic choice to the setup of stochastic choice.