Dodgson's election system elegantly satisfies the Condorcet criterion. However, determining the winner of a Dodgson election is known to be Θ_2~p-complete ([1], see also [2]), which implies that unless P = NP no polynomial-time solution to this problem exists, and unless the polynomial hierarchy collapses to NP the problem is not even in NP. Nonetheless, we prove that when the number of voters is much greater than the number of candidates (although the number of voters may still be polynomial in the number of candidates), a simple greedy algorithm very frequently finds the Dodgson winners in such a way that it "knows" that it has found them, and furthermore the algorithm never incorrectly declares a nonwinner to be a winner.
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机译：Dodgson的选举系统优雅满足CondorCet标准。然而，确定Dodgson选举的获奖者是θ_2〜p-treate（[1]，另见[2]），这意味着除非P = NP没有存在对此问题的多项式时间解决方案，除非多项式层次结构崩溃到NP问题甚至不是在NP中。 Nonetheless, we prove that when the number of voters is much greater than the number of candidates (although the number of voters may still be polynomial in the number of candidates), a simple greedy algorithm very frequently finds the Dodgson winners in such a way that它“知道”它已经找到了它们，此外，该算法从未错误地声明了一个诺维人成为胜利者。
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