 A different kind of rule is Choquet expected utility, also known as cumulative utility (Schmeidler 1989; Gilboa 1987). This rule starts with a function \(v\) which, like a probability function, obeys \(v(E)\in[0, 1],\) \(v(0) = 0,\) \(v(1) = 1,\) and \(A \subseteq B\) implies \(v(A) \le v(A).\) Unlike a probability function, however, \(v\) is non-additive; and \(v\) is not straightforwardly used to calculate an expectation. (Many economists refer to this function as a “non-additive subjective probability function”.). Choquet expected utility is a member of the rank-dependent family (Quiggin 1982, Yaari 1987, Kahneman &amp; Tversky 1979, Tversky &amp; Kahneman 1992, Wakker 2010). Functions in this family let the weight of an event in an act’s overall value depend on both the probability-like element and the event’s position in the ordering of an act, e.g., whether it is the worst or best event for that act. Formally, let \(g' = \{E_1, x_1;\ldots; E_n, x_n\}\) be a re-ordering of act \(g\) from worst event to best event, so that \(u(x_1) \le \ldots \le u(x_n).\) The Choquet expected utility of \(g'\) (and therefore of \(g\)) is: