Journal of Risk and Uncertainty

, Volume 8, Issue 2, pp 167–196 | Cite as

Violations of the betweenness axiom and nonlinearity in probability

  • Colin F. Camerer
  • Teck-Hua Ho


Betweenness is a weakened form of the independence axiom, stating that a probability mixture of two gambles should lie between them in preference. Betweenness is used in many generalizations of expected utility and in applications to game theory and macroeconomics. Experimental violations of betweenness are widespread. We rule out intransitivity as a source of violations and find that violations are less systematic when mixtures are presented in compound form (because the compound lottery reduction axiom fails empirically). We also fit data from nine studies using Gul's disappointment-aversion theory and two variants of EU, which weight separate or cumulative probabilities nonlinearly. The three theories add only one parameter to EU and fit much better.

Key words

expected utility generalized utility risk-aversion prospect theory Allais paradox betweenness disappointment-aversion 

JEL codes

D81 C91 


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Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • Colin F. Camerer
    • 1
  • Teck-Hua Ho
    • 2
  1. 1.Graduate School of BusinessUniversity of ChicagoUSA
  2. 2.Department of Decision SciencesUniversity of PennsylvaniaUSA

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