Skew-symmetric additive representations of preferences (Q1300363)

Let \(S\) be a set of states, \(X\) a set of consequences. Acts are functions from \(S\) into \(X\). An act \(f\) is simple if the set \(f(S)\) is finite. In this paper a generalization of \textit{P. C. Fishburn}'s axiomatization [Utility Theory for Decision Making, Wiley, New York (1970; Zbl 0213.46202); Nonlinear Preference and Utility Theory, John Hopkins University Press, Baltimore (1988; Zbl 0715.90001)] of skew-symmetric additive representations of preferences in decision making under uncertainty is offered from simple to non-simple acts.