On Tue, May 27, 2003 at 06:31:22PM -0400, Nathanael Nerode wrote: > > Do all these perverse cases also require less than 2Q votes to > > be cast? > Sadly, no. They do require less than Q votes to be cast with A above > the default, and nearly all of the other votes to be cast with A equal > to the default. You can have 2Q-3 votes that have explicit ranks for all options, viz: Q-1 ABD Q-2 BDA A beats B, Q-1:Q-@, A beats D, Q-1:Q-2; B beats D, 2Q-3:0. (Any more than that, and you've either got A beats D by >=Q:<blah>, and it makes quorum, or D beats A Q-1:>=Q-1, and A doesn't make it's majority requirement) You can have an additional 2Q-4 votes if your votes are of the form: Q-1 ABD Q-2 DAB 2Q-4 B (A beats B, 2Q-3:2Q-4; A beats D, Q-1:Q-2; B beats D, 3Q-5:Q-2). If you have any more votes: where A > D, then A will make quorum where D > A, then A won't make its majority requirement where B > A, then A won't be the Condorcet winner you can vote A=D > B without contravening those rules, though, for something like: Q-1 ABD Q-2 DAB X B Y (A=D)B with A beats B, 2Q-3+Y:X; A beats D, Q-1:Q-2; B beats D, Q-1+X:Q-2+Y, which is satisfied as long as: X > Y Y > X-2Q+3 In the last election, we had 303 votes that expressed full preferences, which is much greater than 2Q-3 (85); and we had precisely three votes of the form "X=D, X,D > Y". > They also require an electorate with strongly divided, > balanced views on at least two options, and another option which lots of > people rank equal to the default (which gets kicked out). Fundamentally, what it requires is for very few people to express full preferences. There're only two reasons for this: one is that most people don't understand the issue, which isn't what happens in Debian; and the other is that they see some benefit in voting against their true preferences. And for large X and Y, the above example is very unstable; and I don't believe it could realistically be used as a strategy. > So, in this situation, how would you feel if only Q-1 developers voted > for C, but lots of other people voted C at equal rank to D? Tough luck. It's not remotely difficult to get Q developers to rank an option higher than "further discussion". 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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