# Testing Descriptive Utility Theories: Violations of Stochastic Dominance and Cumulative Independence

### Abstract

Choices between gambles show systematic violations of stochastic dominance. For example, most people choose (\$6,.05; \$91,.03; \$99,.92) over (\$6,.02; \$8,.03; \$99,.95), violating dominance. Choices also violate two cumulative independence conditions: (1) If S = (z, r; x, p; y, q) ≻ R = (z, r; x′, p; y′, q) then S‴ = (x′, r; y, p + q) ≻ R″ = (x′, r + p; y′, q). (2) If S′ = (x, p; y, q; z′, r) ≺ R′ = (x′, p; y′, q; z′, r) then S‴ = (x, p + q; y′, r) ≺ R‴ = (x′, p; y′, q + r), where 0 < z < x′ < x < y < y < y′ < z′.

Violations contradict any utility theory satisfying transivity, outcome monotonicity, coalescing, and comonotonic independence. Because rank-and sign-dependent utility theories, including cumulative prospect theory (CPT), satisfy these properties, they cannot explain these results.

However, the configural weight model of Birnbaum and McIntosh (1996) predicted the observed violations of stochastic dominance, cumulative independence, and branch independence. This model assumes the utility of a gamble is a weighted average of outcomes\‘ utilities, where each configural weight is a function of the rank order of the outcome\‘s value among distinct values and that outcome\‘s probability. The configural weight, TAX model with the same number of parameters as CPT fit the data of most individuals better than the model of CPT.