ABSTRACT
Monotonicity is a fundamental assumption of axiomatic decision theories. According to this principle, if two alternatives are otherwise identical, except one has an outcome for at least one nonempty state of nature that is preferred to the corresponding outcome for the other alternative, then the alternative with the better outcome should be preferred. Applied to judgments of the value of gambles, the principle states that the judged value of a gamble should increase monotonically as a function of each outcome, holding everything else constant. As appealing as this axiom is for normative theory, it has been systematically violated in experiments in which subjects judge cash values of gambles. The violation has not been observed in transparent, direct comparisons, but it has been replicated when the gambles are compared to a fixed set of cash values. The violations can be explained by the assumption that decision weights in judgment differ depending on the rank and also on the augmented sign (which is negative, zero, or positive). Violations of branch independence can also be explained by rank-dependent configural weighting. The pattern observed rules out the theory that subjects cancel common outcomes in comparison. The pattern is also opposite that predicted by the inverse-S weighting function used in cumulative prospect theory. Testable properties are suggested to distinguish different models of configural weighting.
