  In 1876, Lewis Carroll proposed a voting system in which the winner is the
candidate who with the fewest changes in voters' preferences becomes a
Condorcet winner---a candidate who beats all other candidates in pairwise
majority-rule elections. Bartholdi, Tovey, and Trick provided a lower
bound---NP-hardness---on the computational complexity of determining the
election winner in Carroll's system. We provide a stronger lower bound and an
upper bound that matches our lower bound. In particular, determining the winner
in Carroll's system is complete for parallel access to NP, i.e., it is complete
for $\thetatwo$, for which it becomes the most natural complete problem known.
It follows that determining the winner in Carroll's elections is not
NP-complete unless the polynomial hierarchy collapses.
