Luce and Narens (Journal of Mathematical Psychology, 29:1–72, 1985) showed that rank-dependent utility (RDU) is the most general interval scale utility model for binary lotteries. It can be easily established that this result cannot be generalized to lotteries with more than two outcomes. This article suggests several additional conditions to ensure RDU as the only utility model with the desired property of interval scalability in the general case. The related axiomatizations of some special cases of RDU of independent interest (the (...) quantile utility, expected utility, and Yaari’s dual expected utility) are also given. (shrink)