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A note on deriving rank-dependent utility using additive joint receipts. (English) Zbl 0847.90024

Summary: R. D. Luce and P. C. Fishburn [J. Risk Uncertain. 4, No. 1, 29-59 (1991; Zbl 0743.90009)] derived a general rank-dependent utility model using an operation \(\oplus\) of joint receipt. Their argument rested on an empirically supported property (now) called segregation and on the assumption that utility is additive over \(\oplus\). This note generalizes that conclusion to the case where utility need not be additive over \(\oplus\), but rather is of a more general form, which they derived but did not use in their article. A. Tversky and D. Kahneman [J. Risk Uncertain. 5, 204-217 (1992)] conjecturing that the joint receipt of two sums of money is simply their sum, criticized that original model because \(\oplus = + \) together with additive utility implies the unacceptable conclusion that the utility of money is proportional to money. In the present generalized theory, if \(\oplus = + \), utility is a negative exponential function of money rather than proportional. Similar results hold for losses. The case of mixed gains and losses is less well understood.

MSC:

91B16 Utility theory

Citations:

Zbl 0743.90009
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References:

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