On Sat, May 24, 2003 at 09:24:34PM -0400, Nathanael Nerode wrote: > Consider if all the people who, in my original example, ranked A=D, > instead ranked A *below* D. > 19x ADB > 19x ABD > 1x BDA > > A vs. B > 38 to 1 > > D vs. A > 20 to 19 Huh? YM A vs D: 38:1. > B vs. D > 20 to 19 > > There's no Condorcet winner. And A meets quorum and wins. If you meant: 19x DAB 19x ABD 1x BDA You have: A beats B, 38:1 B beats D, 20:19 D beats A, 20:19 and under the proposed system, A is dropped for lack of support, and B wins. What are the possible outcomes? A wins, in spite of not having a quorum of support B wins, in spite of A being preferred by a vast majority. D wins, in spite of B being preferred by a clear majority. A is unacceptable, but could easily have been made acceptable by the people who support A getting a single additional vote. This has never been a problem in the past. As A is unacceptable, the qualification against choosing B as the winner is fairly weak. Further choosing D is unacceptable, since that causes process problems in the future: what do we do instead? So choosing B is the least objectionable, which is to say best, course of action. Note that without quorum, A is dropped any way, since it doesn't defeat the default option by its majority requirement, and B wins then too. The way the proposal is constructed, the elector with a casting vote can never choose to void the election if any options are acceptable. > With Manoj's quorum, A is eliminated and B wins by a hair, same as with > the equal rankings. But 38 people prefer A to B and only 1 person > prefers B to A. Now B is implemented. Some people may think that this > is desirable, of course. I certainly don't. A majority of 20:19 think it's more desirable than doing nothing, by assumption. > Consider my original example: > 19x A=DB > 19x ABD > 1x BA=D > > Under Manoj's system, B wins! B is implemented! > A new ballot ("Fix the results of the stupid ballot we just had!") > proposes A vs. "Keep the present system" (B) vs. "more discussion" (D). > The first set of voters hated B and want to get rid of it before > discussing things further, so they change their votes: > 19x ADB > 19x ABD > 1x BA=D So, if the first set of voters find A acceptable, why didn't they vote that way originally? They could have, quite easily. > --- > The problems are not really present for the Technical Committee, since > the quorum is 2. For technical reasons, this cannot cause any odd > behavior. Not due to quorum perhaps, but you can still get: 3 ABD 3 DAB 2 BDA A beats B, 6:2; B beats D 5:3; D beats A 5:3. A doesn't make its majority requirement, and is eliminated, so B wins. Cloneproof SSD alone would have eliminated B beats D and D beats A, leaving A or D as the winner. > -- > It also seems unlikely for the aforementioned problems to happen in a GR > when the number of voters is >=2*R, where R is the quorum requirement. > > Unfortunately, it *can* happen with an arbitrarily large number of > voters. Yes, and it's possible for a meteorite to hit master.debian.org just as the vote's closing and for D to thus win by default, even if _everyone_ voted for A! It's not a likely thing to happen both historically, and because in the balance, it's beneficial for you to express full preferences, wherever possible. I don't think you can actually get any problems with quorum with more than 12R voters, actually. That's 570 of 1000 developers voting, so isn't particularly unbelievable. You also need a linearly increasing number of options to manage this, afaict; I think you need at least 7 options to have a vote where an option beats the winner, but doesn't make quorum, with 12R voters, as well as an utterly unbelievable distribution of preferences. > How? When there are lots of options and lots of rankings equal to > the default option, as well as a highly splintered electorate. You'll note that we try to avoid having a splintered electorate -- you know, decision by consensus and all that; and have a voting system that's designed to find a compromise that's as acceptable as possible. Cheers, aj -- Anthony Towns <email@example.com> <http://azure.humbug.org.au/~aj/> I don't speak for anyone save myself. GPG signed mail preferred. ``Dear Anthony Towns: [...] Congratulations -- you are now certified as a Red Hat Certified Engineer!''
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