Common Consequence Conditions in Decision Making under Risk
 George Wu,
 Richard Gonzalez
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Abstract
We generalize the Allais common consequence effect by describing three common consequence effect conditions and characterizing their implications for the probability weighting function in rankdependent expected utility. The three conditions—horizontal, vertical, and diagonal shifts within the probability triangle—are necessary and sufficient for different curvature properties of the probability weighting function. The first two conditions, shifts in probability mass from the lowest to middle outcomes and middle to highest outcomes respectively, are alternative conditions for concavity and convexity of the weighting function. The third condition, decreasing PrattArrow absolute concavity, is consistent with recently proposed weighting functions. The three conditions collectively characterize where indifference curves fan out and where they fan in. The common consequence conditions indicate that for nonlinear weighting functions in the context of rankdependent expected utility, there must exist a region where indifference curves fan out in one direction and fan in the other direction.
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 Title
 Common Consequence Conditions in Decision Making under Risk
 Journal

Journal of Risk and Uncertainty
Volume 16, Issue 1 , pp 115139
 Cover Date
 19980401
 DOI
 10.1023/A:1007714509322
 Print ISSN
 08955646
 Online ISSN
 15730476
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 Rankdependent expected utility
 prospect theory
 commonconsequence effects
 fanning out
 fanning in
 probability weightingfunction
 Industry Sectors
 Authors

 George Wu ^{(1)}
 Richard Gonzalez ^{(2)}
 Author Affiliations

 1. Graduate School of Business, University of Chicago, 1101 E. 58th Street, Chicago, IL, 60637
 2. Dept. of Psychology, University of Michigan, Ann Arbor, MI, 48109