The complexity of Kemeny elections

Kemeny proposed a voting scheme which is distinguished by the fact that it is the unique voting scheme that is neutral, consistent, and Condorcet. Bartholdi, Tovey, and Trick showed that determining the winner in Kemeny's system is NP-hard. We provide a stronger lower bound and an upper bound matching the lower bound, namely, we show that determining the winner in Kemeny's system is complete for P||NP, the class of sets solvable via parallel access to NP.