Hello all, I've been trying to catch up on the highlights of controversies past in regard to voting methods. I personally find the Condorcet methods attractive, and have been persuaded by my reading online that Schulze Method is the best for my interests. However, I have seen good arguments both for and against votes against and margins as standards for measuring beatpath strengths. I will note here that I am tentatively in favor of allowing ties and truncations, as well as allowing each voter to indicate whether they wish any particular tie to count as 0 or 0.5 votes. But here is my fundamental question. Is there some way to combine the strengths of these two methods of measuring victories/defeats? One simple method (perhaps too simple?) which occurs to me would be to analyze the ballots by Schulze both with margins and with votes against, and when they both choose the same winner, you'd be finished, but where they choose different winners, choose the candidate who won the original pairwise comparison between them. How often would either Schulze Method variation choose more than one winner in the absence of a numerical tie? Most of the time it would appear that Schulze is fairly decisive, so I think this as a fairly reliable way to choose a winner. Another thought I've been playing with is a way of combining the votes against with the margin to express a composite value. The first way I thought of was to simply add the margin and votes against together. This would give you a value that is heavily weighted by the votes given to the victor, yet also takes into account the margin of the pairwise matching. I had problems with seeing a result of 51:49 as equal to either 51:1 or to 3:1, not to mention all the possibilities between. And as the election considered grows in voters, the extreme possibilities grow too (although, I have to wonder, just how disproportionate can the votes get and still have the candidates all in the Smith set?). If, however, we were to add the votes, then you narrow the range of equivalent votes by almost half for competitions were some voters truncate the two candidates in pairwise competition (for example, for 51:49 the most extreme equivalent is 27:1 since 51+(51-49)S and 27+(27-1)S. All other comparisons fall between these ranges of votes against and margins. Of course, if we say this is a possible alternative to margins or votes against, it can in some instances choose a winner in a cycle who is different from both the votes against and margins winner. After thinking about this combo measure for a little while, I found that another idea kept intrusively popping to mind. Another way to positively combine the measures would be multiplication. Wouldn't the large elections be fun to calculate (Oh look, A's beatpath to B is only a trillion, guess B wins that one...). Actually, the math is simplistic, it's just the numbers that are large. Multiplication of margins by votes against tends to really spread out the results, keeping much lower the number of beatpaths of equal value, and has the nice effect that margins have of automatically giving ties a beat value of 0. I haven't looked too deeply at this multiplicative option yet (as I tend to think of these things on the commute to and from work, the multiplication begins to get a little distracting when I go above 10 voter examples (20 is not too bad, but still...). My purpose in proposing these combinational ideas is to try to give value to the two concepts of what constitutes the strength of a pairwise result. I think both have merit, and information about voter choices that's worth preserving. I would greatly appreciate commentary from all about the possible strengths and weaknesses of these proposed measures. If these ideas have been suggested in the past, I apologize for re-inventing them and ask if someone could point me towards the discussion on them. As far as I have been able to find in my short time looking into condorcet methods, they have not been proposed before quite like this. I would like to thank all the contributors to this list from 1998 on for posting their thoughts, ideas, and debates, from which I have learned and leaned upon in trying to figure this stuff. Glen Finney
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