"A person is said to prefer in the stochastic dominance sense one lottery over outcomes over another lotter[y] over outcomes if the probability of his (at least) first choice being selected in the first lottery is greater than or equal to the analogous probability in the second lottery, the probability of his at least second choice being selected in the first lottery is greather than or equal to the analogous probability in the second lottery, and so on, with at least one strict inequality. This (partial) preference relation is used to define straightforwardness of a social choice function that maps profiles of ordinal preferences into lotteries over outcomes. Given a prior probability distribution on profiles this partial preference ordering (taking into account the additional randomness) is used to induce a partial preference ordering over social choice functions for each individual. These are used in turn to define ex ante Pareto undominated (efficient) social choice functions. The main result is that it is impossible for a social choice function to be both ex ante efficient and straightforward. We also extend the result to cardinal preferences and expected utility evaluations."