The probabilistic serial rule is one of the most well-established and desirable rules for the random assignment problem. We present the egalitarian simultaneous reservation social decision scheme – an extension of probabilistic serial to the more general setting of randomized social choice. We consider various desirable fairness, efficiency, and strategic properties of social decision schemes and show that egalitarian simultaneous reservation compares favorably against existing rules. Finally, we define a more general class of social decision schemes called simultaneous reservation, that contains egalitarian simultaneous reservation as well as the serial dictatorship rules. We show that outcomes of simultaneous reservation characterize efficiency with respect to a natural refinement of stochastic dominance.