An axiomatic treatment of three qualitative decision criteria

The need for computationally efficient decision-making techniques together with the desire to simplify the processes of knowledge acquisition and agent specification have led various researchers in artificial intelligence to examine qualitative decision tools. However, the adequacy of such tools is not clear. This paper investigates the foundations of maximin, minmax regret, and competitive ratio, three central qualitative decision criteria, by characterizing those behaviors that could result from their use. This characterizaton provides two important insights: (1)under what conditions can we employ an agent model based on these basic qualitative decision criteria, and (2) how “rational” are these decision procedures. For the competitive ratio criterion in particular, this latter issue is of central importance to our understanding of current work on on-line algorithms. Our main result is a constructive representation theorem that uses two choice axioms to characterize maximin, minmax regret, and competitive ratio.

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