Cognitive Foundations of Probability

Itzhak Gilboa and David Schmeidler

No 1340, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: Prediction is based on past cases. We assume that a predictor can rank eventualities according to their plausibility given any memory that consists of repetitions of past cases. In a companion paper, we show that under mild consistency requirements, these rankings can be represented by numerical functions, such that the function corresponding to each eventuality is linear in the number of case repetitions. In this paper we extend the analysis to rankings of events. Our main result is that a cancellation condition a la de Finetti implies that these functions are additive with respect to union of disjoint sets. If the set of past cases coincides with the set of possible eventualities, natural conditions are equivalent to ranking events by their empirical frequencies. More generally, our results may describe how individuals form probabilistic beliefs given cases that are only partially pertinent to the prediction problem at hand, and how this subjective measure of pertinence can be derived from likelihood rankings.

Keywords: Bayesian prior; case-based decision theory; qualitative probabilities (search for similar items in EconPapers)
JEL-codes: D80 (search for similar items in EconPapers)
Pages: 33 pages
Date: 2001-12
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Citations: View citations in EconPapers (1)

Published in Mathematics of Operations Research (2002), 27: 68-81

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Related works:
Working Paper: Cognitive Foundations of Probability (2002)
Working Paper: Cognitive Foundations of Probability (1999)
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