On the foundations of qualitative decision theory

This paper investigates the foundation of maximin, one of the central qualitative decision criteria, using the approach taken by Savage (Savage 1972) to investigate the foundation and rationality of classical decision theory. This approach asks `which behaviors could result from the use of a particular decision procedure?' The answer to this question provides two important insights: (1) under what conditions can we employ a particular agent model, and (2) how rational is a particular decision procedure. Our main result is a constructive representation theorem in the spirit of Savage's result for expected utility maximization, which uses two choice axioms to characterize the maximin criterion. These axioms characterize agent behaviors that can be modeled compactly using the maximin model, and, with some reservations, indicate that maximin is a reasonable decision criterion.