 The constraint can more helpfully be put as follows: In comparing two acts, one ignores the values of their respective cdf’s on the set of outcomes with respect to which they agree. It is easily verified that the Allais preferences are consistent with this principle. Given probabilistic sophistication, Ordinal Independence can itself be derived from a constraint on preferences over acts known as “Comonotonic Independence”, presented in  Subsection 3.2.1  below. Wakker (2010) offers a textbook introduction to RDU and Cumulative Prospect Theory, as well as to related treatments of the issues discussed in the next section.