Expected consumer's surplus as an approximate welfare measure

Except for a knife-edge case of preferences, the percentage error from using the change in expected consumer's surplus (ECS) to approximate the willingness to pay for a change in the distribution of a random price is unbounded, in contrast to Willig's (Am Econ Rev 66:589-597; 1976) famous approximation result for nonrandom prices. If the change is smooth on the space of random variables, and either the initial price is nonrandom or state-contingent payments are possible, then the change in ECS locally approximates the willingness to pay well. Unfortunately, this smoothness fails in some important applications.