Conditional non-expected utility preferences induced by mixture of lotteries: a note on the normative invalidity of expected utility theory

Gebhard Geiger ()
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Gebhard Geiger: Technical University of Munich

Annals of Operations Research, 2020, vol. 289, issue 2, No 15, 448 pages

Abstract: Abstract This research note is concerned with static choices between alternative mixtures of lotteries with one common mixture component and identical mixture weights. It is shown that the common component induces a conditional preference relation on the underlying lottery space with given (unconditional) preference structure. Induced preferences of this type arise in the comparisons with which the independence axiom of expected utility theory is specifically concerned. Given a few obvious properties of the induced preferences, two basic results are obtained: first, the conditionalisation operation is an order-preserving isomorphism, and, secondly, if the conditional preferences satisfy stochastic dominance preference, they necessarily violate the independence axiom. Together, the two results preclude any possibility of postulating independence consistently for static decision making under risk. The independence axiom is thus generally invalid as a normative principle of rational risky choice.

Keywords: Rational choice; Risky choice; Normative theory; Expected utility; Independence axiom (search for similar items in EconPapers)
JEL-codes: D81 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10479-020-03528-5

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