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Cognitive Foundations of Probability

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Author Info

  • Itzhak Gilboa

    (Tel Aviv University)

  • David Schmeidler

    (Tel Aviv 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.

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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1340.

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Length: 33 pages
Date of creation: Dec 2001
Date of revision:
Publication status: Published in Mathematics of Operations Research (2002), 27: 68-81
Handle: RePEc:cwl:cwldpp:1340

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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

Related research

Keywords: Bayesian prior; case-based decision theory; qualitative probabilities;

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Cited by:
  1. Enriqueta Aragones & Itzhak Gilboa & Andrew Postlewaite & David Schmeidler, 2003. "Accuracy vs. Simplicity: A Complex Trade-Off," UFAE and IAE Working Papers 564.03, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).

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