Deterministic voting rules are notoriously susceptible to strategic voting. We propose a new solution to this problem for large electorates. For any deterministic voting rule, we can design a stochastic rule that asymptotically approximates it in the following sense: for a sufficiently large population of voters, the stochastic voting rule (i) incentivizes every voter to reveal her true preferences and (ii) produces the same outcome as the deterministic rule, with very high probability.