Gambles are recursively generated from pure payoffs, events, and other gambles, and a preference order over them is assumed. Weighted average utility representations are studied that are strictly increasing in each payoff and for which the weights depend both on the events underlying the gamble and the preference ranking over the several component payoffs. Basically two results are derived: a characterization of monotonicity in terms of the weights, and an axiomatization of the representation. The latter rests on two important conditions: a decomposition of gambles into binary ones and a necessary commutativity condition on events in a particular class of binary gambles. A number of unsolved problems are cited. As a theory of choice between pairs of either risky or uncertain alternatives, subjective expected utility (SEU) is widely acknowledged to be normatively compelling, but not fully descriptive of behavior. Much that is wrong with SEU was anticipated early by Allais (1952/1979, 1953) and Ellsberg (1961), but relatively massive amounts of additional evidence were accumulated during the 1970s and early 1980s. Some of the data, especially those having to do with how the gambles are framed and the evidence for intransitivities (preference reversal phenomenon), went considerably beyond the earlier work. For an up-to-date statement of the issues from an economic perspective, see Machina (1987)and Weber and Camerer (1987), and for detailed list of the references concerning empirical tests, see Segal (1987a, p. 194). One obvious possibility is to generalize the representation, keeping some of its attractive axiomatic features but omitting those that seem to be the source o
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