A well-known theorem of Debreu about additive representations of preferences is applied in a non-additive context, to characterize continuous subjective expected utility maximization for the case where the probability measures may be non-additive. The approach of this paper does not need the assumption that lotteries with known (objective) probability distributions over consequences are available.

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Keywords additive representation, expected utility, utility theory
Persistent URL dx.doi.org/10.1016/0304-4068(89)90002-5, hdl.handle.net/1765/23226
Wakker, P.P.. (1989). Continuous subjective expected utility with non-additive probabilities. Journal of Mathematical Economics, 18(1), 1–27. doi:10.1016/0304-4068(89)90002-5