Dear Mike, you wrote (5 March 2005): > Markus is right to point out that, as I've defined it, FBC has a > problem when there's a tie. As Markus pointed out, a single voter > can change the outcome only by changing a definite win to a tie, > or changing a tie to a definite win. > > FBC, as defined so far, has a problem with a tie. If the way that > you could get your best outcome is by breaking a tie, and getting > a certain outcome, then, if you don't do so, that same candidate > might win the tie anyway, and so what you get when you break the > tie isn't better than anything that you could get wihtout doing so. > On the other hand, if, by voting someone over your favorite, you > could make a tie, then you aren't electing with certainty someone > who is better than anyone you could otherwise have gotten, since > you aren't electing anyone with certainty. > > The obvious and easy way out of this is to replace "voter" with > "set of voters who have the same peferences and vote in the same > way". > > That fixes the problem. Thanks for pointing the problem out, > Markus.
FBC says: > By voting a less-liked candidate over his/her favorite, > a voter should never gain an outcome that he/she likes > better than every outcome that he/she could get without > voting a less-liked candidate over his/her favorite. Suppose there is more than one favorite candidate. Suppose A and B are some of these favorite candidates. When this voter has to vote B over A, then is this a violation of FBC? Accoding to the above definition of FBC, this is not a violation of FBC since B is not a "less-liked candidate". But is this also in spirit of FBC? Markus Schulze ---- Election-methods mailing list - see http://electorama.com/em for list info