The logsum formula, which provides the expected maximum utility for the multinomial logit model, is often used as a measure of welfare. We provide here a closed form formula of the welfare measure of an individual who has not access to his first-best choice, but has access to his rth-best...

We show that the number of individuals selecting their worst alternatives within a finite set of alternatives can be written as an alternating sum of the number of individuals having their best choice within subset of alternatives. The identities are then applied to random utility models,...