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Probabilistic independence axiom

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Listed:
  • Pavlo Blavatskyy

    (Montpellier Business School)

Abstract

One of the most well-known theories of decision making under risk is expected utility theory based on the independence axiom. The independence axiom postulates that decision maker’s preferences between two lotteries are not affected by mixing both lotteries with the same third lottery (in identical proportions). The probabilistic independence axiom (also known as the cancelation axiom) extends this classic independence axiom to situations when a decision maker chooses in a probabilistic manner (i.e., she does not necessarily prefer the same choice alternative when repeatedly presented with the same choice set). Probabilistic choice may occur for a variety of reasons such as unobserved attributes of choice alternatives, imprecision of preferences, random errors/noise in decisions. According to probabilistic independence axiom, the probability that a decision maker chooses one lottery over another does not change when both lotteries are mixed with the same third lottery (in identical proportions). This paper presents a model of probabilistic binary choice under risk based on this probabilistic independence axiom. The presented model generalizes an incremental expected utility advantage model of Fishburn (Int Econ Rev 19(3):633–646, 1978) and stronger utility model of Blavatskyy (Theory Decis 76(2):265–286, 2014).

Suggested Citation

  • Pavlo Blavatskyy, 2021. "Probabilistic independence axiom," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 46(1), pages 21-34, March.
    • Handle: RePEc:pal:genrir:v:46:y:2021:i:1:d:10.1057_s10713-019-00046-8
    DOI: 10.1057/s10713-019-00046-8
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    References listed on IDEAS

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    1. Fishburn, Peter C, 1978. "A Probabilistic Expected Utility Theory of Risky Binary Choices," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 19(3), pages 633-646, October.
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    More about this item

    Keywords

    Decision making; Risk; Independence axiom; Probabilistic choice;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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