>The idea of the linearity condition is simply that the statements being >checked are all linear inequalities. In the very simplest case of plurality >voting, candidate A would win if: f(votes for A) - f(votes for B) > 0 AND f(votes for A) - f(votes for C) > 0 AND etc. for all other candidates
--a good name for that would be "polyhedral" voting methods. I don't know why, since it seems to be an excellent concept -- and you've shown it is useful -- but nobody (?) seems to have discussed/named it before. I was certainly aware (and probably many others too) that practically everything was a polyhedral method, but few or no people ever actually found a use for that observation before. Well... actually I can think of some uses, but they were of a quite different character. Numerous authors have used it to assess probabilities of phenomena via polyhedral-volume computations, and I've used it to find the "best/simplest" election examples of phenomena by solving a linear program to find the example. You're using it to make logical deductions to prove theorems. >As for "*" vs. "x" for multiplication --well, jeez, just use no symbol at all, AB = A*B, just like everybody else. But if you insist on a symbol use cdot. (I do use * when forced to write in un-typeset ASCII. But if you have a math typesetting program, why?) >style... --well, you're calling it style, but I think there is more to it than that. There's good reasons for what you call style. What *I* would label with the word style, is stuff for which there is NOT really good reasons, and it really is more of a matter of personal choice. Like use of the first person singular. E.g. theorem statements ought to be self-contained standalone readable. Definitions ought to be precise. This is not a mere matter of style in my view. If they aren't then you're abusing the words; they aren't real, it is just a sham. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step) and math.temple.edu/~wds/homepage/works.html ---- Election-Methods mailing list - see http://electorama.com/em for list info
