“Making Book Against Oneself,” the Independence Axiom, and Nonlinear Utility Theory

An individual with known preferences over lotteries can be led to accept random wealth distributions different from his initial endowment by a sequential process in which some uncertainty is resolved and he is offered a new lottery in place of the remaining uncertainty. This paper examines the restrictions that can be placed on an individual's preferences by axioms that stipulate that such a process not be able to generate a new wealth distribution that is prima facie inferior to the original. The relationship of these axioms to the independence axiom of von Neumann and Morgenstern and to the quasi convexity of preferences in the wealth distribution are explored.