 The representation theorem for REU combines conditions from two existing theorems (Machina &amp; Schmeidler 1992, Köbberling and Wakker 2003), replacing the separability condition with two weaker conditions. One of these conditions fixes a unique probability function of events (Machina &amp; Schmeidler’s “Strong Comparative Probability”, 1992) and the other fixes a unique risk function of probabilities; the latter is a restricted version of the separability condition (Köbberling &amp; Wakker’s [2003] “Comonotonic” Tradeoff Consistency; see  section 4.3.2).  Since the representation theorem derives a unique probability function, a unique risk function, and a unique (up to positive affine transformation) utility function, it separates the contribution of diminishing marginal value and global sensitivity to a given preference ordering. One can disprefer mean-preserving spreads as a result of either type of risk-aversion, or a combination of both.