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

Artikel

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Journal: Annals of Operations Research ; ISSN: 1572-9338 ; Volume: 289 ; Year: 2020 ; Issue: 2 ; Pages: 431-448 ; New York, NY: Springer US

Classification and Topics

• Classification: Allgemeines, Wissenschaft ; Criteria for Decision-Making under Risk and Uncertainty
• Subject: Rational choice ; Risky choice ; Normative theory ; Expected utility ; Independence axiom

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Geiger, Gebhard
• Event: Veröffentlichung
• (who): Springer US
• (where): New York, NY
• (when): 2020

Further information

• DOI: doi:10.1007/s10479-020-03528-5
• Last update: 10.03.2025, 11:43 AM CET