I characterize the set of implementable allocation functions in the standard one dimensional mechanism design environment where the relationship between private information and payoffs is possibly non-monotone. The characterization is useful in two aspects. First it leads to a rather mild...

The Axiom of Monotonicity (AM) is a necessary condition for a number of expected utility representations, including those obtained by de Finetti (1930), von Neumann and Morgenstern (1944) and Savage (1954). The paper reports on experiments that directly test AM by eliminating strategic...