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Violations of the betweenness axiom and nonlinearity in probability

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Abstract

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.

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Authors and Affiliations

  1. Graduate School of Business, University of Chicago, USA

    Colin F. Camerer

  2. Department of Decision Sciences, University of Pennsylvania, USA

    Teck-Hua Ho

Authors
  1. Colin F. Camerer
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  2. Teck-Hua Ho
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Additional information

The financial support of the National Science Foundation (SES 88-09299) is gratefully acknowledged. Comments from Larry Epstein, Rob Porter, John Quiggin, several anonymous referees, and seminar participants at the University of Pennsylvania were helpful.

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Camerer, C.F., Ho, TH. Violations of the betweenness axiom and nonlinearity in probability. J Risk Uncertainty 8, 167–196 (1994). https://doi.org/10.1007/BF01065371

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