Abstract In social choice settings with strict preferences, random dictatorship rules were characterized by Gibbard [1977] as the only randomized social choice functions that satisfy strategyproofness and ex post efficiency. In the more general domain with indifferences, RSD (random serial dictatorship) rules are the well-known and perhaps only known generalization of random dictatorship. We present a new generalization of random dictatorship for indifferences called Maximal Recursive (MR) rule as an alternative to RSD. We show that MR is polynomial-time computable, weakly strategyproof with respect to stochastic dominance, and, in some respects, outperforms RSD on efficiency.