Journal of Risk and Uncertainty

, Volume 30, Issue 1, pp 21-62

First online:

Ranked Additive Utility Representations of Gambles: Old and New Axiomatizations

  • R. Duncan LuceAffiliated withUniversity of California Email author 
  • , A. A. J. MarleyAffiliated withUniversity of Victoria and University of Groningen

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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: ranked 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: idempotence, general event commutativity*, coalescing, gains decomposition, 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 some of the primary results.


coalescing component summing event commutativity gains decomposition ranked additive utility ranked weighted utility utility representations