First, about how to treat short rankings, if you've ranked X and you haven't ranked Y, then it's reasonable to say that you've ranked X over Y. I hope that's how that's interpreted in the debian count rules.
The rank-counting procedure now in use by debian carries out Condorcet's suggestion that if there's 1 candidate who, when compared separately to each one of the others, is ranked over him/here by more voters than vice-versa, then that candidate should win. That's called "Condorcet's Criterion". But it isn't really Condorcet's method, because Condorcet proposed a complete method, a method that specified what to do when there isn't 1 candidate who pairwise-beats each one of the others. Actually, he made 2 proposals about that, and either could be called Condorcet's method. But of course there are other ways of solving "circular ties", where no 1 candidate beats each one of the others: Copeland suggested that we subtract the number of pairwise-defeats that a candidate has from the number of pairwise-victories that he has, and call that his Copeland score. The winner is the candidate with highest Copeland score. There's often a tie. Dodgson suggested that we elect the candidate who could be made to beat everyone by reversing the fewest individual pairwise preference votes. Black suggested that we use Borda's point system when there's a circular tie. And so on... The method that debian is currently using, solving circular ties by the Alternative Vote elimination system is equivalent to something proposed by George Hallett, in a book in 1926, and so it could be called "Hallett's method". What all these methods have in common is that they're pairwise-count methods, and they're Condorcet Criterion methods, meaning that they comply with Condorcet's Criterion. But they aren't Condorcet's method. They're Copeland's method, Dodgson's method, Black's method, and Hallett's method. (Incidentally, Dodgson was the author better known as Lewis Carroll). What Condorcet proposed were 2 methods that stepwise drop weakest defeats. I described several interpretations of what Condorcet meant, when I wrote to this mailing list about half a year ago. Since it's so brief, let me repeat one of the circular tie solutions that I defined that time, a good interpretation of what Condorcet meant with one of his proposals: Sequential Dropping (SD): Drop the weakest defeat that is in a cycle. Repeat till there's an unbeaten candidate. (B's defeat by A is measured by how many people ranked A over B). *** Condorcet's method has many advantages over the other circular tie solutions, in regards to majority rule, and avoidance of strategy problems, such as the lesser-of-2-evils problem and the spoiler problem. I'll refrain from repeating here the somewhat wordier definition of the other interpretation of Condorcet's "bottom-up" proposal, because I defined it here about half a year ago. I called it Schwartz Sequential Dropping (SSD). The most widely accepted interpretation of Condorcet's other stepwise weak-defeat-dropping proposal is slightly wordier: Drop the strongest defeat that's the weakest defeat in a cycle. Repeat till there are no cycles remaining. Probably the motivation for that isn't obvious, so let me tell you its original wording: Tideman's method: 1. Arrange all the defeats in a list in order of their strength. 2. Starting with the strongest defeat, consider, in turn, each defeat in the list. If a defeat is in a cycle with stronger defeat, then drop it. 3. Continue down the list in that way till no cycles remain. *** But actually, it was originally worded in terms of "keeping" or "locking-in" defeats, rather than dropping them: 1. Arrange all the defeats in a list in order of their strength. 2. Starting with the strongest defeat in the list, consider, in turn, each defeat in the list. Keep the list being considered if it isn't in a cycle with stronger defeats that have been kept. Otherwise, skip it. 3. Continue down the list in that way till no cycles remain. *** So, in a meaningful sense, one is keeping all the strongest defeats possible. *** For committee voting, SSD & Tideman are excellent. In committees, where there are so few voters that pairwise ties or equal defeats are likely, Tideman has one known advantage over SSD: A "clone set" is a set of candidates who are adjacently-ranked in every voter's ranking. And let's say that a clone set must have more than 1 member. Independence from Clones Criterion (ICC): Removing a candidate from a clone set shouldn't change the matter of whether the winner comes from that clone set. SSD, but not Tideman, can fail ICC in small committee elections where there are pairwise ties or equal defeats. In the example that I'm aware of, this just means that there are situations where Tideman will return a tie between two clone sets, while SSD is decisive and picks a winner, and the matter of which clone set the winner comes from can be influenced by internal defeats in the clone sets. The purist doesn't like that, and prefers Tideman's tie, and its resort to a random tie-solution. But if SSD's choice seems arbitrary to the clone-purist, maybe it could be said that it's no worse than flipping a coin, unless the tied clone sets situation is considered so likely as to influence people's voting, or to deter "clone" candidates from running. Anyway, I've defined SD, SSD, & Tideman. The latter two are considered better when pairwise ties or equal defeats are likely, in small committee voting. Tideman satisfies the purist who wants absolute compliance with the clone criterion, even under small-committee conditions. *** Well, now that I've written such a long letter, and defined SD & Tideman (in 3 wordings), why not repeat the definition of SSD: 1. an "unbeaten set" is a set of candidates none of whom are beaten by anyone outside that set. 2. An "innermost unbeaten set" is an unbeaten set that doesn't contain a smaller unbeaten set. SSD: Drop the weakest defeat that is between members of an innermost unbeaten set. Repeat till there's an unbeaten candidate. *** If members of debian want to perfect their voting system, then I suggest changing the count rule, the circular tie solution to SD, or, especially, SSD or Tideman. Though I posted the criteria that these methods meet, and which distinguish them from other pairwise-count methods, I'll re-post them, or send them by individual e-mail, upon request. Mike Ossipoff ________________________________________________________________________ Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com
