So far, we have considered preference relations on distributions defined in terms of a fixed utility function u. In this section, we focus on the question whether one distribution is preferred over another, regardless of the choice of a particular utility function.

For simplicity, we take S = ℝ as the set of possible payoffs. Let M be the set of all μ ∈ M1(ℝ) with well-defined and finite expectation

Recall from Definition 2.35 that a utility function on ℝ is a strictly concave and strictly increasing function u : ℝ → ℝ. Since each concave function u is dominated by an affine function, the existence of m(μ) implies the existence ...

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