Forest wrote: >(1) Bubble sort starts from the top and works down: If the Borda order is > A > B > C , then Bubble compares A and B first, and then advances C as > far up as possible, one comparison at a time. So in circular ties > Bubble can alter the Borda order if the Borda order is opposite to the > cyclic order.
My mistake. So my examples were wrong. In a three way cyclic tie, 3rd in Borda can never win; whoever wins the first vs. second matchup wins. For more complicated cyclic ties, the lowest candidate who beats every candidate above them wins. This seems reasonable, I suppose. >(2) Borda's strategic problems are no worse than those of Ranked Pairs > when it comes to three way circular ties. In other words, Black is as > good as Ranked Pairs in three way races. I beleive this is not the case. Ranked Pairs is (at least in some cases) more clone independent. Adding a candidate to the race that is listed just after one of the leaders on every ballot will boost that leading candidate's Borda count, while not changing anything in the pairwise matchups. If this boost brings the candidate from third to first in a three-way cyclic tie, they will win the election where they would have lost it. This is not to say that Ranked Pairs is certainly better; only that it is very different and I don't see any intuitive reason why the outcomes of the Ranked Pairs method of breaking cyclic ties would bear any strong resemblance to the BSBS method of breaking cyclic ties. I would not be surprised to see an example where BSBS does a better job than Ranked Pairs of producing an intuitively correct result. Finally, let me add that I don't think Ranked Pairs is the best tie-breaker either... I think Mike's Shwartz Sequential Dropping is better. The only differences as far as I can tell are that 1) You only deal with the Smith Set 2) You consider number of voters in favor of the defeat, not the margin of the defeat. Months before I joined this list, I corresponded briefly with Mike Ossipoff and Russ Paielli about examples I had cooked up that seemed to create problems for Condorcet. At the time, I did not realize the distinction between Ranked Pairs and SSD, and some of my seemigly undesireable results hinged on this. -Adam
