 A problem with the function \(r\), as defined above, is that the transformed probabilities which it gives rise to will not add up to 1 except in the trivial case when r is the identity function (Fishburn 1978). To solve this problem, Quiggin (1982) introduced the rule of maximizing anticipated utility (also called utility with rank dependent probabilities). Instead of replacing \(p(x)\) by a function of the individual probability, \(r(p(x))\), he replaced it by a function that also depends on the other probabilities and utilities involved in the problem. The outcomes are first ordered from worst to best, which results in a vector \(\langle x_1, x_2 ,\ldots , x_n\rangle\) of outcomes, such that \(u(x_1) \leq u(x_2) \leq \ldots \leq u(x_n)\). A decision weight can then be assigned to each outcome, taking into account both its probability and its position in the ranked sequence of outcomes. Since the decision-weight can be different for outcomes with the same probability, Fishburn’s trivialization result does not apply here. There is evidence indicating that rank-dependent utility models may be more empirically adequate than prospect theory (Harrison and Ross 2017).