A note on deriving rank-dependent utility using additive joint receipts

Abstract

Luce and Fishburn (1991) derived a general rank-dependent utility model using an operation ⊕ of joint receipt. Their argument rested on an empirically supported property (now) calledsegregation and on the assumption that utility is additive over ⊕. This note generalizes that conclusion to the case where utility need not be additive over ⊕, but rather is of a more general form, which they derived but did not use in their article. Tversky and Kahneman (1992), conjecturing that the joint receipt of two sums of money is simply their sum, criticized that original model because ⊕=+ together with additive utility implies the unacceptable conclusion that the utility of money is proportional to money. In the present generalized theory, if ⊕=+, 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.