Dodgson's method

Dodgson's method is a Condorcet method that ranks a candidate X according to the number of times adjacent candidates have to be swapped on a ballot (not necessarily the same ballot each time) to make X the Condorcet winner. The candidate with the least number of necessary swaps wins.

If X is the Condorcet winner, the number of swaps is zero, so the method passes Condorcet. However, determining the winner in the general case is complete for parallel access to NP, and thus NP-hard.

For more information, see Dodgson's method on Wikipedia.

Criterion compliances
Dodgson's method passes the Condorcet criterion. It fails the independence of clones criterion, the Smith criterion, the monotonicity criterion, and also fails the homogeneity criterion: an election with 100 voters may return a different result to an election with 10 voters, even if the relative size of the factions is the same.

P. C. Fishburn proposed a variant that passes homogeneity and where the winner can be found in polynomial time, but the variant fails the other three criteria mentioned above.