# Why is Schulze the most popular Condorcet election method?

It's been my impression that when people are discussing "Condorcet voting", they often implicitly mean the Schulze/beatpath method.

Wikipedia's "Use of Condorcet voting" list also seems to be mostly Schulze, and there's an even longer list at Schulze method § Users.

What features/benefits does it have over other Condorcet systems?

• hey, endo. nice to see you over here. i don't think that Schulze would be more popular than Ranked Pairs if either were considered for governmental elections. it's very important that simplicity, both in the voting action on the ballot and in the tabulation procedure that identifies the winner, be in the code. RP is far simpler that Schulze and if there are only 3 candidates in the Smith Set, RP and Schulze will elect the same candidate. Mar 20 '17 at 20:19

Your link notes that Ranked Pairs fulfills the most voting system criteria of the Condorcet-compliant systems. Schulze is second, missing only Local Independence of Irrelevant Alternatives of the criteria that Ranked Pairs meets. Schulze is faster to compute as the number of alternatives grows than Ranked Pairs (N^3 is better than N^4). Ranked Pairs has the second worst time complexity, after Kemeny-Young (factorial; N!).

More practically, Markus Schulze seems to have been more active on mailing lists where software programmers participated (citations on the Wikipedia page under references). So there are more Schulze implementations and open source software communities were more familiar with Schulze than Ranked Pairs. Which is of course self-reinforcing, as any time someone needs software to calculate a Condorcet-winner, it's easy to find Schulze. So, mostly superior marketing by its inventor.

• It would appear from the other answer that you are correct. :D Feb 19 '17 at 20:59
• Arguably, the Schulze method is also inherently quite marketable to people with a strong math/programming/combinatorics background. It's just the widest path problem applied to the directed graph of mutual preferences in order to get a transitive partial ordering, and this turns out to have several fairly beautiful nontrivial equivalent formulations. Oct 26 '20 at 16:51

Both methods, the Schulze method and Tideman's ranked pairs method, satisfy many academic criteria (e.g. monotonicity, resolvability, reversal symmetry, independence of clones). The difference between the Schulze method and the ranked pairs method is that the Schulze method tries to find the best candidate (without violating any of the mentioned criteria) while the ranked pairs method tries to find the best collective ranking (without violating any of the mentioned criteria). However, being good in finding a winner and being good in finding a collective ranking isn't the same. Someone who argues that the purpose of an election is to find a winner might argue that the worst pairwise defeat of the winner should be as weak as possible and, therefore, might prefer the Schulze method. Someone who argues that the purpose of an election is to find a collective ranking of all candidates might argue that the worst pairwise defeat that is in contradiction to the collective ranking should be as weak as possible and, therefore, might prefer ranked pairs.

In my opinion, the sole purpose of an election is to find a winner, even though many election methods give a collective ranking as an intermediate result. The fact, that many election methods and many academic criteria are defined in terms of rankings rather than in terms of winners, is rather a relic from the history of social choice theory than a real argument. The fact, that some Condorcet supporters argue that the purpose of an election is to find a collective ranking, makes Condorcet supporters look stupid. For example, when Condorcet supporters argue that IRV is a lousy election method because it can happen that the last eliminated candidate differs from that candidate who would have won if the original winner had not run, then IRV supporters reject this argument as obviously irrelevant; and I guess that most other people would agree with the IRV supporters on this point.

• Wikipedia says that Schulze produces a collective ranking, though. "Therefore, if several positions are available, the method can be used for this purpose without modification, by letting the k top-ranked candidates win the k available seats." Is this not a recommended application, then? Jun 25 '18 at 15:34
• The Schulze method provides an excellent partial ordering of the candidates. Ranked pairs needs to be iterated by successively removing the winner to produce a ranking, and it's not clear to me that it is better than doing the same thing with Schulze. Oct 26 '20 at 16:57

The Schulze method satisfies many academic criteria (e.g. monotonicity, resolvability, reversal symmetry, independence of clones) so that it is a very good election method even when there happens to be no Condorcet winner. Most Condorcet advocates make the mistake that they concentrate on the Condorcet criterion exclusively so that, when they fail to convince the audience about the importance of the Condorcet criterion, they immediately run out of arguments.

• Markus, your reputation with me is far more than "1". Mar 20 '17 at 20:20
• But compared with Ranked Pairs specifically, does that apply? Jul 5 '17 at 6:48