My previous letter showing why BeatpathWinner, Cloneproof SSD, & PC are monotonic was hurried, and not as complete & explicit as it should have been. So now I'm saying it in a more complete way: Say the method is BeatpathWinner, and you uprank X without changing the order of the other candidates in your ranking. How can that affect beatpaths? When you rank X over some other candidate Y, whom you'd previously ranked over X, there are several ways that can affect a beatpath: You could reverse X's defeat by Y. That could eliminate a beatpath to X, or it could create a beatpath from X. That couldn't cause X to no longer have a beatpath win over another candidate. Of course it could also make X the BeatsAll winner, or stop Y from being BeatsAll winner. That couldn't make X lose. Or, if X already beats Y, then newly ranking X over Y increases the magnitude of the XY defeat, and could thereby strengthen a beatpath from X to another candidate (which could be Y). Of, if Y beats X, but your XY reversal doesn't reverse that defeat, the fact that you're no longer voting Y over X weakens the magnitude of that defeat, and thereby could weaken a beatpath to X. That, too, can't cause X to no longer have a beatpath win against another candidate. Can you tell me some way in which upranking X without changing the order of the other candidates could make another candidate the BeatsAll winner, stop X from being BeatsAll winner, or increase the strength of a beatpath to X, or decrease the strength of a beatpath from X? Can you tell me how upranking X could cause X to no longer have a beatpath win against another candidate? If it can't cause those results then BeatpathWinner is monotonic. Cloneproof SSD is equivalent to BeatpathWinner, and so it's monotonic. If anyone has an example in which BeatpathWinner or CSSD is nonmonotonic, then will you post it? Mike Ossipoff _________________________________________________________________ Send and receive Hotmail on your mobile device: http://mobile.msn.com
