Institute for Mathematical Behavioral Sciences

A number of classical as well as quite new utility representations for gains are explored with the aim of understanding the behavioral conditions that are necessary and sufficient for various subfamilies of successively stronger representations to hold. Among the utility representations are: additive, weighted, rank-dependent (which includes cumulative prospect theory as a special case), gains decomposition, subjective expected, and independent increments, where denotes something new in this article. Among the key behavioral conditions are consequence monotonicity, idempotence, general status-quo event commutativity, coalescing, gains decomposition, consequence-event substitutability, and component summing. The structure of relations is sufficiently simple that certain key experiments are able to exclude entire classes of representations. For example, the class of rank-dependent utility models is very likely excluded because of empirical results about the failure of coalescing. Figures 1-3 summarize all but two of the network of primary results.