Blake said: I note that you don't usually define the Schwartz set as a procedure. Your usual definition of SSD is really a combination of the two techniques. I reply: True, now that you mention it. The goal definition is briefer, in both instances. I really like the brevity of the goal definition of Ranked Pairs (RP). I guess mention of a ranking avoids the need of mentioning cycles. But many people will wonder what an output ranking has to do with the selection of a single winner. Of course any defeat that's in a cycle is contradicted, nullified by the other defeats in the cycle, and that justifies getting rid of all cycles, and that could be said in an explanation of why we're interested in a transitive ranking of the candidates. Still, I wonder if people wouldn't accept it better in the procedure form, which is also fairly brief, and which needn't mention a ranking, but does have to speak of cycles, or contradiction among defeats. I didn't like the relative vagueness of speaking of contradiction, but, as you may have said, someone can always ask how a defeat can be contradicted by other defeats, and is easily answered by showing him/her a cycle. So maybe I'd use the procedure that I posted, but replace the cycle wording with "keep the defeat if it isn't contradicted by already-kept defeats". Maybe that's the most acceptable RP definition. Blake continued: > I think that ease of implementation is a very weak argument. It isn't as if we don't know how to implement Ranked Pairs, we do. Check out ( http://vote.sourceforge.net/rpweb/rpweb.html). And programmers should be willing to implement a harder algorithm if it makes it simpler for the general public. For a successful method, the number of people who write software to tabulate it will be minuscule compared to the number who will want to know how it's making its selection. I reply: I agree if you're talking about public elections. But when you propose a voting system to a small committee, the committeemembers' acceptance is going to be related to how complicated the count is. And RP is plenty complicated in small committees. Complicated, elaborate count rules, and long program, compared to CSSD or BeatpathWinner. Committee- members considering a new count rule are much closer to the count than public voters are. I believe that RP(wv) is a fine proposal for public elections. Only polling will really tell whether RP(wv), CSSD, or SSD is more acceptable for public elections. I'd expect that, for public elections, where SSD & CSSD choose the same, SSD's stopping rule is more obvious, making it a better public proposal. But since CSSD is better for committees, and committees & organizations provide precedent, maybe CSSD would make it to public acceptance before SSD would. Maybe RP(wv) will win in the public polling, because of its brief definition. Every bit as brief & simple as IRV. Blake continued: One of the reasons I like the goal-based definition of Ranked Pairs, is that it encourages people to view the complete ranking as a satisfactory result. If they want, they can check it against the definition, which is easier than finding the correct ranking. If you describe a method in terms of a procedure, people are going to want to have every step of the procedure as the result. I reply: True, if people don't have a problem about an output ranking. Blake continued: That's a problem, because you say you want to advocate CSSD, but then use the BeatpathWinner implementation, which I assume means Floyd's algorithm. But Floyd's algorithm won't let you see the procedure being carried out, it just gives you a final answer. I reply: True. When I've recommened CSSD to small committees, I've always suggested the BeatpathWinner implementation, because committeemembers are closer to the count than public voters are. In public elections, programmers could of course implement CSSD by its own defining procedure if they wanted to. Or the BeatpathWinner procedure could be used, and ,if necessary, people could testify that BeatpathWinner always chooses the same winner that CSSD chooses. As you said, though, RP's output ranking is easily checked. I'd said: >Also, CSSD always chooses from the initial Schwartz set, but >Tideman doesn't. But in public elections Tideman virtually always >does. Blake replied: I don't see why anyone should care one way or the other. If you could convince me that there was some practical problem with choosing outside the Schwartz set, I'd agree with you. Even if I could imagine the public caring, this would be a point in your favour. But the Schwartz set is just another obscure mathematical construct. I reply: I'm not saying that there's a practical problem with choosing outside the initial Schwartz set. But choosing in the Schwartz set has compelling plausibility, you must admit. If there's a beatpath from A to B, but no beatpath from B to A, then the sequence of public statements that says that A is better than B isn't contradicted. The whole reason why we need circular tiebreakers is because of that kind of contradiction. Without one, we have a collective public statement that A is better W, and W is better than X and X is better than Y, and Y is better than Z, and Z is better than B, and so it's reasonable to say that A is indirectly better than B. Unless that's contradicted by a return beatpath, we should accept what that sequence of public statements is saying. The Schwartz set of course has 2 definitions, the beatpath definition and the unbeaten set definition. We could look at it in terms of an unbeaten set, and point out the special status had by a set of candidates none of whom are beaten by anyone outside that set. It's obvious to someone with no prior experience with voting systems that there's something special, especially deserving of winning, about the candidates in that unbeaten set. Markus suggested a way to ensure that RP(wv) always chooses from the initial Schwartz set. Other ways include deleting the non-Schwartz candidates as soon as the count indentifies them, or saying that their defeats must be kept. Of course that's one more rule for a method that already is far too wordy in the form needed by small committees. In public elections there's no need to do anything about the Schwartz set, since RP always chooses from the Schwartz set in public elections (absent the rare pair tie). When I was going to count the ballots for the EM polls last summer, it was of course necessary to ask the RP proponents to tell me how they wanted to deal with equal defeats during the count. No one really explained at that time how they wanted it done. I understand that Blake has a website article about that though. Blake continues: My phrasing is as follows: Ranked Pairs gives the ranking of the options that always reflects the majority preference between any two options, except in order to reflect majority preferences with greater margins. I reply: Sounds great. Maybe that's how I'd propose it, pending more conversations or polling. Except, of course, that I'd just say "magnitude" or "strength", instead of "margins". Blake continues: I usually precede this with some description of what a ranking is, and if I really want to be rigorous, what I mean by saying that a ranking reflects a majority preference. Let's say I have victories A>B 20, B>C 19, C>A 18. Now, consider the ranking A>B>C. The only majority it doesn't reflect is C>A. But any ranking with C>A will either not reflect A>B or not reflect B>C, both of which are included in A>B>C. So, it's all right to have A ranked over C, because this is done in order to reflect majority preferences with greater margins. So, A>B>C is the Ranked Pairs ranking. I comment: It's interesting to look at the different ways that RP & CSSD choose. AB2, BC3, CA10, AD20, DC30, BD10 B has by far the weakest defeat, and is chosen by CSSD, SSD & PC. The initial Schwartz set is the whole candidate-set. But though B's defeat is weakest, A's defeat is contradicted by the strongest defeats. Keeping A's defeat amounts to overruling the voters who voted for AD20 & DC30. Dropping the weakest defeat vs keeping the strongest defeats. When RP is worded by saying to drop the strongest defeat that's the weakest defeat in a cycle, that wording raises unnecessary questions about why we start by dropping a strong defeat. But, if we're looking at it in that way, in terms of dropping, we aren't dropping A's defeat because _it_ is stronger. We're dropping it because the defeats that contradict it are the strongest. As I said, I prefer wording it in terms of keeping, rather than dropping. Also, maybe the goal definition would be better accepted, due to its even greater brevity, if people don't object to the output ranking. Mike Ossipoff _________________________________________________________________ Get your FREE download of MSN Explorer at http://explorer.msn.com/intl.asp.
