Ranking opportunity sets in a simple intertemporal framework

We extend the problem of ranking subsets (opportunity sets) of a set of alternatives to an intertemporal setting, whereby the agent makes a sequence of choice decisions over time. In particular, we show in a simple two-period model that an agent who satisfies five plausible axioms ranks opportunity sets in a lexicographic fashion. That is, the agent ranks opportunity sets based solely on the relative desirability of their first-period alternatives, and only if the first-period alternatives are thought equally desirable does the agent consider the second-period alternatives. We discuss this strong time-discounting result and the role of the axioms, and also show that the popular “independence” axioms employed in the existing “static” literature are inconsistent with some reasonable axioms regarding intertemporal choice.