An Axiomatic Approach
This chapter focuses on case-based reasoning. It offers an axiomatic approach to the following problem: given a database of observations, how should different eventualities be ranked? The approach is complementary to the Bayesian approach at two levels: first, it may offer an alternative model of prediction, when the information available to the predictor is not easily translated to the language of a prior probability. Second, the approach may describe how a prior is generated. The chapter is organized as follows. Section 2 presents the formal model and the main results. Section 3 discusses the relationship to kernel methods and to maximum likelihood rankings. Section 4 presents a critical discussion of the axioms, outlining their scope of application. Finally, Section 5 briefly discusses alternative interpretations of the model, and, in particular, relates it to case‐based decision theory.
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