Mike Ossipoff wrote: > PC (Minmax) can be stated in a non-iterative way, and I once believed > that that meant it's monotonic. But I seem to have heard that Dodgson > is nonmonotonic, even though it isn't iterative.
It depends on how Dodgson is defined. The definition that I prefer is monotonic; it's equivalent to summing the columns of the margins matrix and choosing the candidate with the smallest column sum. The other definition I've seen counts the number of reversals needed in the actual ranked ballots; it's nonmonotonic. An example (from Hannu Nurmi's book Comparing Voting Systems): 5:A>B>C>D>E 2:B>A>D>E>C 4:B>E>D>A>C 8:D>A>C>E>B A would require 3 preference reversals (switching with D) to become the Condorcet winner and any other candidate would require more (D would need to swap with B on two ballots, requiring four actual preference swaps), so A is the winner of the nonmonotonic version of Dodgson. If the two B>A>D>E>C voters uprank A, the votes become 5:A>B>C>D>E 2:A>B>D>E>C 4:B>E>D>A>C 8:D>A>C>E>B Now D becomes the winner using this version of Dodgson. D wins both times using the monotonic version of Dodgson (and every other Condorcet method I've tried). A wins both times using Borda. -- Rob LeGrand [EMAIL PROTECTED] http://www.aggies.org/honky98/ __________________________________________________ Do You Yahoo!? Send FREE video emails in Yahoo! Mail! http://promo.yahoo.com/videomail/
