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DOI: 10.23952/cot.2026.6
Received Octobe 29, 2024; Accepted November 27, 2024; Published online January 20, 2026
Abstract. While expected utility maximization and its foundations in the Savage Axioms play a major role in normative economics and Bayesian statistics, the axiomatic foundations of expected utility maximization have been the subject of extensive criticism over the years in terms of their descriptive ability to explain actual behavior in laboratory experiments. As a result, behavioral economists do not accept expected utility maximization as descriptive of observed consumer behavior. But the Savage Axioms have been substantially weakened and rendered more widely descriptive of observed behavior by replacing the usual Riemann integral with the Choquet [14] integral. In addition, the observed behavior under the weakened assumptions is relevant to behavior under uncertainty in the Frank Knight [47] sense, rather than the more restrictive context of behavior under risk with known probabilities. The behavioral implications of expected utility maximization with Choquet integration reduce to the more restrictive axiomatic foundations for Riemann integration only if probabilities always sum to exactly 1.0. By permitting probabilities to sum to more than or less than 1.0, called “nonadditive probabilities,” Choquet integration is consistent with far more general observed behavior than is consistent with the Savage Axioms, as has been recognized in Tversky and Kahneman’s Prospect Theory [64]. But the mathematical foundations for Choquet integration and its uses in modeling behavior under uncertainty are based on sophisticated mathematics on Riesz space. Cerreia-Vioglio et al. [8] provided a general integral representation for nonadditive probabilities defined on an Archimedean Riesz space, based on the fundamental work of Aliprantis et al. [1,2,3]. Aliprantis introduced Riesz space into the field of economics and established the relevancy of Riesz space to Choquet integration and thereby to behavioral economics We shall show that Aliprantis’s deep theoretical research in this area has had formidable consequences for advancing behavioral economics in many applications in a rigorous but very practical manner. This approach provides a formal mathematical improvement that is compatible with Allais’ [4] and Ellsberg’s [29] paradoxes, which Savage’s [61] theorem fails to explain.
How to Cite this Article:
W.A. Barnett, K. Ding, Expected utility maximization under weakened assumptions consistent with behavioral economics, Commun. Optim. Theory 2026 (2026) 6.