Uncovered Set Choice Rule

I study necessary and sufficient conditions for a choice function to be rationalised in the following sense: there exists a complete asymmetric relation <i>T</i> (a <i>tournament</i>) such that for each feasible (finite) choice situation, the choice coincides with the uncovered set of <i>T</i>. This notion of rationality explains not only cyclical and context dependent choices observed in practice, but also provides testable restrictions on observable choice behavior.