Rank- and sign-dependent linear utility models for finite first-order gambles

Abstract

Finite first-order gambles are axiomatized. The representation combines features of prospect and rank-dependent theories. What is novel are distinctions between gains and losses and the inclusion of a binary operation of joint receipt. In addition to many of the usual structural and rationality axioms, joint receipt forms an ordered concatenation structure with special features for gains and losses. Pfanzagl's (1959) consistency principle is assumed for gains and losses separately. The nonrational assumption is that a gamble of gains and losses is indifferent to the joint receipt of its gains pitted against the status quo and of its losses against the status quo.