Condorcet method: Difference between revisions

Sequential comparison is the fastest generalized way to determine the Condorcet winner, when one exists, from the pairwise matrix: order all of the candidates in any manner desired, pairwise compare the first two, eliminate the loser of the match upmatchup, and repeat until only one candidate remains. This requires ((number of candidates) - 1) pairwise comparisons, since for each comparison one candidate is eliminated, and all but one candidate must be eliminated. To check whether a Condorcet winner exists in a given election, do the previous procedure and then check whether thisthe remaining candidate wins all of their pairwise matchups; this requires ((number of candidates) - 2) pairwise comparisons in the worst case, though if the ordering of the candidates in the procedure is done in such a way as to put candidates more likely to be Condorcet winners higher in the ordering, then in the best case 0 pairwise comparisons are required, since if the first candidate in the ordering turns out to be the Condorcet winner, all of their pairwise comparisons have already been done. Condorcet winners may often have a lot of 1st choice votes, especially in less contested elections, so it may be even fasterbest to firstorder checkthe whethercandidates thosedescending typesby order of candidates1st choice votes, then 2nd choice votes, etc. These procedures can winbe allused ofeven theirfor pairwiseCondorcet matchupsPR methods by considering each winner set to be a candidate.

*'''[[Smith//Score]]''' chooses the candidate with the highest summed or average score in the Smith Set. [[Condorcet//Score]] chooses the [[Utilitarian winner|Score winner]] when no Condorcet winner exists. (These can only be done with rated ballots, or with ranked ballots modified to include approval thresholds).