The error in my definition of voting a candidate higher is obvious. It's obvious that other people's ballots have nothing to do with whether John votes some candidate higher. Equally obvious is the way that the definition should have been written: A voter, John, votes Smith higher if he changes how he marks Smith in such a way that it's possible to contrive a fixed* way for John to mark the other candidates, such that after the change, John's ballot votes Smith over a candidate over whom it didn't vote him before the change. *By a fixed way of marking the other candidates, I mean a way that John doesn't change, except where such change is an unavoidable result of changing how he marks Smith. [end of definition] Of course the reason why I accidentally wrote it in terms of other people's votes was because that's how my definition of voting Smith over Jones is written. It seems to me that my definition of Monotonicity, with its supporting definitions, is satisfactory, but of course there's always the possibility there being some other error that I haven't noticed. If someone comes up with another bizarrely unproposable method in order to find a "problem" with that Monotonicity definition, then I'd point out that Monotonicity is not going to be discarded, and that it's necessary to have some definition of that criterion. I don't mean to imply that I claim that my definition can't be improved on. I merely post it as a possible, workable way of defining Monotonicity. Mike Ossipoff _________________________________________________________________ MSN Photos is the easiest way to share and print your photos: http://photos.msn.com/support/worldwide.aspx
