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Cognitive Foundations of Probability

Author

Listed:
  • Itzhak Gilboa

    (TAU - Tel Aviv University)

  • David Schmeidler

    (TAU - 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 à 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.

Suggested Citation

  • Itzhak Gilboa & David Schmeidler, 2002. "Cognitive Foundations of Probability," Post-Print hal-00752283, HAL.
    • Handle: RePEc:hal:journl:hal-00752283
    DOI: 10.1287/moor.27.1.65.330
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    Cited by:

    1. Tsoukias, Alexis, 2008. "From decision theory to decision aiding methodology," European Journal of Operational Research, Elsevier, vol. 187(1), pages 138-161, May.
    2. Pe[combining cedilla]ski, Marcin, 2011. "Prior symmetry, similarity-based reasoning, and endogenous categorization," Journal of Economic Theory, Elsevier, vol. 146(1), pages 111-140, January.
    3. 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).

    More about this item

    Keywords

    Probability; ranking of events; likelihood ranking;
    All these keywords.

    JEL classification:

    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General

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