There are a number of cases in which individuals do not expect to find out which outcome occurs. The standard von Neumann-Morgenstern Expected Utility model cannot be used in these cases, since it does not distinguish between lotteries for which the outcomes are observed by the agent and lotteries for which they are not. This paper provides an axiomatic model that makes this distinction. A representation theorem is then obtained. This framework admits preferences for observing the outcome, and preferences for remaining in doubt. Doubt-proneness and doubt-aversion are defined, and the relation between risk-aversion, caution and doubt-attitude is explored. The model builds on the standard vNM framework, but other frameworks can also be extended to allow for preferences for observing the outcomes and preferences for remaining in doubt. A methodology for this extension is also provided. This framework can accommodate behavioral patterns that are inconsistent with the vNM model, and which have let to significantly different models. In particular, this framework accommodates self-handicapping, in which an agent chooses to impair his own performance. It also admits a status-quo bias, even though it does not allow for framing effects. In a political economy setting, voters have incentive to remain ignorant even if information is costless.