Rank-And-Sign Dependent Linear Utility Models for Finite First- Order Gambles.

For finite first-order gambles--mappings from finite event partitions into a set of pure consequences--axioms are given that lead to a representation that combines features of prospect theory and the general rank-dependent theories. The axioms include four structural ones that insure a certain richness to the domain of choice. There are four rationality ones: (i) monotonicity of preference with respect to consequences in binary gambles; (ii) preference and joint receipt of gambles form an ordered concatenation structure in which preferences are transitive and both monotonicity and accumulativity of joint receipt hold relative to preference, and, in addition, three special axioms that relate the positive and negative domains; (iii) an accounting equivalence to the effect that indifference obtains between a gamble and its decomposition into subgambles that involve only consequences of the same sign; and (iv) another accounting equivalence that any gamble whose consequences are of one sign is judged indifferent to the joint receipt of the consequence closest to the status quo plus the gamble obtained by "subtracting" that consequence from all of the others. And finally we assume one non-rational decomposition axiom that possibly is descriptive in character. It says in essence that a mixed gamble is thought of as the joint receipt of its positive part pitted against the status quo and of its negative part pitted against the status quo. This important assumption is especially in need of empirical investigation. The resulting representation in a sense includes all previous ones for first-order gambles, including SEU, prospect theory, and rank-dependent theories.