Dale Sheldon writes: > I don't find the system to be unintuitive. Perhaps "unintuitive" is the wrong word. It makes perfect sense in theory, but looking at a table of votes and figuring out the results is far from obvious. > The complication comes, and this vote has some great examples, of what do > to when A beats B, B beats C, and C beats A, as happened, when Subdivision > beat Zamboni Wars, Zamboni Wars beat Moonshot, and Moonshot beat > Subdivision. > > The base Condorcet method doesn't address how to handle so-called > "Condorcet ties", but the Ranked Pairs method, which was used for this > vote, breaks the tie by, essentially, ignoring the "weaker" wins; ZW beat > MS by 15, and SD beat ZW by 4, while MS beat SD by only 2. (It's > explained a bit more wordily for precision's sake, but that's the meat of > it.) And here's that URL again: http://condorcet.org/rp/ Unfortunately, the Ranked Pairs method does not say what to do when all the wins in a tied group are equal[1], which also happened here: Pylon beat Zamboni Wars by 2, Zamboni Wars beat Penguin Soccer by 2, and Penguin Soccer beat Pylon by 2. This is where Zarf's tiebreaker (which is not part of the standard Ranked Pairs method) comes in, by looking at which games beat more other games, or lost to fewer, but I'm still a little fuzzy about exactly how and when this tiebreaker is applied. And the fact that Zarf's new program gives slightly different results from his old program, and Timothy Hunt's procedure appears to be slightly different from either of Zarf's programs, makes me think that there are still some kinks to work out (even though they did all give the same result here). I'm also a little worried about problems that could result from allowing incomplete ballots. For example, suppose Trip Away had only appeared on one ballot (because, say, no one else could figure out how to play from the rules), but it was ranked first on that ballot, above all the other games. It would then win the competition, because its margin over every other game would be 1, and there would be no inconsistencies. In practice, I highly doubt that anything like this would happen. But I think it shows that it's important to have enough players play every game (or, more precisely, to have every game played by enough players). Perhaps a game should be required to appear on some minimum percentage of ballots or be disqualified? > That said, it was a _very_ close contest, and there's no such thing as a > "perfect" voting system; but Condorcet Ranked Pairs is a fair sight better > than most, in my opinion. Perhaps, but the issue here is Condorcet Ranked Pairs With Incomplete Ballots And Zarf's Tiebreaker. I'm sure we can either show that it's sound or tweak it until it is, but I'm not quite there yet. (By the way, my reservations about this method do not at all apply to using it in "real-life" elections, where the ratio of voters to candidates is several orders of magnitude higher, and where you only need one winner instead of a total ordering. The issues discussed here would practically never occur in that situation, and I'm fully in favor of advocating for preference voting as a vast improvement over our current broken electoral systems.) --dougorleans@xxxxxxxxx [1] Actually, the ranked pairs website does say what to do in the case of ties: resolve them randomly. http://condorcet.org/rp/details.shtml Obviously that's unsatisfactory here.