On the axiomatization of qualitative decision criteria

Qualitative decision tools have been used in AI and CS in various contexts, but their adequacy is still unclear. To examine this question, our work employs the axiomatic approach to characterize the properties of various decision rules. In the past, we presented a constructive representation theorem for the maximin decision criterion, and we characterized conditions under which an agent can be viewed as adopting a qualitative decision-making approach (consisting of beliefs, goals, and a qualitative decision criterion). In this paper we show that the maximin representation theorem applies to two additional decision criteria: minmax regret and competitive ratio, and with slight modifications, to a third one, maximax. In addition, we characterize conditions under which an agent with a given qualitative utility function can be ascribed beliefs when we assume it adopts maximin as its decision criterion.