Voting is commonly used as a method for aggregating information in crowdsourcing and human computation. In many settings, one would like to use voting rules which can be efficiently elicited, preserve voter privacy, and are robust to strategic manipulation. In this paper, we give algorithms which elicit approximate winners in a way which provably satisfies all three of these requirements simultaneously. Our results hold for tournament voting rules, which we define to be the voting rules which can be expressed solely as a function of the table of pairwise comparisons containing the number of voters preferring one candidate to another. Tournament voting rules include many common voting rules such as the Borda, Copeland, Maximin, Nanson, Baldwin, Kemeny-Young, Ranked Pairs, Cup, and Schulze voting rules. Our results significantly expand the set of voting rules for which efficient elicitation was known to be possible and improve the known approximation factors for ε-strategyproof voting in the regime where the number of candidates is large.
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