Maximax, leximax, and the demanding criterion

Following the characterizations provided by Barberà and Jackson [Barberà, S., Jackson, M.O., 1988. Journal of Economic Theory 46, 34–44] for the maximin, the leximin, and the protective criterion, we examine the consequences of replacing convexity in their list of axioms by concavity, which means considering risk-loving instead of risk-averse agents. This yields characterizations of the maximax, the leximax and a new criterion which we term demanding criterion. We concentrate on the latter and demonstrate the independence of the axioms used for its characterization.