Case-Based Decision Theory

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Abstract
This paper suggests that view that decision-making under uncertainty is, at least party, case-based. We propose a model in which cases are assumed as primitives, and provide a simple axiomatization of a decision rules which chooses a "best" act based on its past performance in "similar" cases. Each act is evaluated by the sum--over cases in which it was chosen--of the product of the similarity of the past case to the problem at hand and the utility level that resulted from this act in the past. As in expected utility theory, both the utility and the similarity functions may be derived from preferences and the latter are represented by (the maximization of) a sum of products. However, there are some crucial differences between case-based decision theory and expected utility theory. In the former: -- every two acts are evaluated over completely different (and disjoint) histories of cases; -- neither probabilities nor states of the world are assumed as primitives. Moreover, the theory does not distinguish between certain and uncertain acts; -- the notions of "satisfiying" decisions and aspiration levels pop up naturally from the axiomatic derivation of case-based decisions. The paper also discusses various aspects, variations and applications of the basic model.

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