Joint receipt and Thaler's hedonic editing rule

Abstract

We consider a rule of ‘hedonic editing’ suggested by R.H. Thaler and others to describe how people evaluate the joint receipt of two separate quantities of a real variable x. Let U be a continuous and increasing utility function on x. We refer to x≥0 as a gain, x≤0 as a loss, fix U(0)=0, and denote by x⊕ y the joint receipt of x and y. The hedonic editing rule says that U(x ⊕y) = max{U(x + y), U(x) + U(y)} so that U( x ⊕ y) is the larger of the utility of the integrated sum of x and y, and the sum of the utilities of x and y considered separately. The paper explains structures of U constrained by hedonic editing. Two main cases are analyzed. Case (I) assumes that U is concave in gains and convex in losses. Case (II) assumes that U is concave separately in gains and in losses. Each main case divides into six subcases according to the limiting relations among the slopes of U at ±0 and ±∞. These partition the behavior of U in the mixed ( x>0, y<0) joint-receipt region into two subregions of integration and segregation. The paper also axiomatizes the cases with assumptions about ( R , ⊕, ≥) from which a suitable U can be constructed. Each main case uses a few axioms satisfied by all its subcases. Special axioms are then invoked for the different subcases.