Inductive Inference: An Axiomatic Approach

Itzhak Gilboa and David Schmeidler

No 1339, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: A predictor is asked to rank eventualities according to their plausibility, based on past cases. We assume that she can form a ranking given any memory that consists of finitely many past cases. Mild consistency requirements on these rankings imply that they have a numerical representation via a matrix assigning numbers to eventuality-case pairs, as follows. Given a memory, each eventuality is ranked according to the sum of the numbers in its row, over cases in memory. The number attached to an eventuality-case pair can be interpreted as the degree of support that the past case lends to the plausibility of the eventuality. Special instances of this result may be viewed as axiomatizing kernel methods for estimation of densities and for classification problems. Interpreting the same result for rankings of theories or hypotheses, rather than of specific eventualities, it is shown that one may ascribe to the predictor subjective conditional probabilities of cases given theories, such that her rankings of theories agree with rankings by the likelihood functions.

Keywords: Inductive inference; case-based reasoning; case-based decision theory; maximum likelihood (search for similar items in EconPapers)
JEL-codes: D80 (search for similar items in EconPapers)
Pages: 45 pages
Date: 2001-12
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Published in Econometrica (2003) 71: 1-26

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Journal Article: Inductive Inference: An Axiomatic Approach (2003)
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Working Paper: Inductive Inference: An Axiomatic Approach (2002)
Working Paper: Inductive Inference: An Axiomatic Approach (2002)
Working Paper: Inductive Inference: An Axiomatic Approach (2001)
Working Paper: Inductive Inference: an Axiomatic Approach (1999)
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