This paper investigates the restrictions on the indifference map that are implied by alternative assumptions about consumer behavior under uncertainty and, conversely, the restrictions on consumer behavior under uncertainty that are implied by alternative assumptions about the indifference map. It is shown, for instance, that if the individual is to be risk neutral at all incomes and price ratios in a given neighborhood, the income-consumption curves must be linear, and if all income-consumption curves are linear, there exists a cardinal representation of utility which is linear in income. The cases of constant relative risk aversion, constant absolute risk aversion, and quadratic utility functions are also investigated.