An axiomatic model of preferences over lotteries is developed. It is shown that this model is consistent with the Allais Paradox, includes expected utility theory as a special case, and is only one parameter $(\beta)$ richer than the expected utility model. Allais Paradox type behavior is identified with positive values of $\beta$. Preferences with positive $\beta$ are said to be disappointment averse. It is shown that risk aversion implies disappointment aversion and that the Arrow-Pratt measures of risk aversion can be generalized in a straight-forward manner, to the current framework.