>>But I think it's reasonable to assume that >>when we refer to changing X's rating, that doesn't include changing >>someone > >else's rating too..." > >Mike is right: it IS reasonable to assume that when we refer to changing >X's >rating, that doesn't include changing someone else's rating too. > I realize that in Plurality or in rank-balloting, changing how we mark one candidate can automatically change how we mark another candidate. So I should have said that changing how we mark one candidate should, reasonably, not include _avoidably_ changing how we mark another candidate. By how we mark a candidate, I mean how we vote him, determined without regard to or comparison to how we vote other candidates on the ballot. Examples are what rank position we give to him, what points rating we give to him, whether or not we vote for him. Sure, the rank position that we give to him invites comparisons to other candidates, but it's a number that we give to him that can be looked at without considering other candidates. Here's a possible way to define voting a candidate higher: A voter, John, changes his ballot to vote Smith higher if he changes how he marks Smith on his ballot in such a way that it's possible to contrive other voters' ballots* so that, when we then make that change, Smith, on John's ballot, is then voted over a candidate over whom he wasn't voted before the change. *unchanging ballots [end of definition] As Richard said, of course unforseen problems can lurk in a definition. When they do, we work them out when we find them. Of course in rank-balloting or Plurality, when you vote Smith higher that might mean that you automatically thereby vote Jones lower, as Joe pointed out. Here's an attempt to define Monotonicity: If, by a certain set of ballots, candidate Smith wins, then if we modify some of the ballots by changing how they mark Smith, in such a way as to vote him higher without voting anyone else lower or higher except where that's an unavoidabe result of voting Smith higher, then, after we've made that change, Smith shouldn't lose. [end of definition] One could add a similar paragraph about when Smith loses and someone votes him lower, but it wouldn't be necessary. Maybe that definition could be made more brief, or replaced by something more brief. Possibly it has a flaw that I haven't noticed, of course. Mike Ossipoff _________________________________________________________________ Chat with friends online, try MSN Messenger: http://messenger.msn.com
