We characterize the partial orderings induced by the most common risk measures and compare them to the partial orderings induced by first and second order stochastic dominance, respectively. We show which risk measures are consistent in the sense that they induce the same partial orderings as stochastic dominance. We also demonstrate which risk measures exhibit the property that stochastic dominance among risky choices imply consistency, and whether the reverse is true. Finally, we find that tail conditional expectation does not meet these consistency criteria.