Reduction invariance and Prelec's weighting functions

Within the framework of separable utility theory, a condition, called reduc tion invariance, is shown to be equivalent to the 2-parameter family of wei ghting functions that Prelec (1998) derived from the condition called compo und invariance. Reduction invariance, which is a variant on the reduction o f compound gambles, is appreciably simpler and more easily testable than co mpound invariance, and a simpler proof is provided. Both conditions are gen eralized loading to more general weighting functions that include, as speci al cases, the families of functions that Prelec called exponential-power an d hyperbolic logarithm and that he derived from two other invariance princi ples. However, of these various families, only Prelec's compound-invariance family includes, as a special case, the power function, which arises from the simplest probabilistic assumption of reduction of compound gambles. (C) 2001 Academic Press.