Truth-revealing voting rules for large populations

We propose a new solution to the problem of strategic voting for large electorates. For any deterministic voting rule, we 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 arbitrarily high probability. We then apply these results to obtain an implementation in Bayesian Nash equilibrium.