EM list-- It's occurred to me that yesterday's definition of strategy doesn't apply easily to Plurality & Approval. Instead of fixing it, I'd like to leave it out. Here's how I'd define defensive & offensive strategy: Defensive strategy: If electing a certain candidate is the goal of a majority of the voters, and some members of that majority vote in a way intended to elect him, that's defensive strategy. If keeping a certain candidate from winning is the goal of a majority of the voters, and some members vote in a way intended to keep him from winning, that's defensive strategy. (I'd like to add a statement that protecting the win of a SCW is defensive strategy too, but for now, when I say "defensive strategy", I mean it as defined above. Till such time as someone says that it would make sense to them to add the SCW clause). Offensive strategy: A voter uses offensive strategy if he votes in a way intended to take victory from a SCW & give it to someone else whom he likes better. [end of those 2 definitions] Again, I realize that, at least in voting systems other than Plurality, voters seldom have only the goal of electing one particular candidate. But hypothetical situations can be presented in which that's the case, and in real elections people's voting often approaches that character. Condorcet Criterion: I'd said that that criterion is always defined to pass nothing or to pass Plurality. It is often written that way, but I can't say it always is. It needn't be. With the understanding that "sincere voting" needs definition, here's how that criterion could be stated: If everyone votes sincerely, the SCW should win. Seamlessly defining sincere voting to apply to all methods isn't as easy as it sounds. Here's an initial try: Not reversing a sincere preference, and not leaving unexpressed any sincere preferences or ratings which the voting system would allow to be expressed in addition to those preferences already expressed. With that definition, the Condorcet Criterion applies to all methods, and Plurality & Approval don't pass. The definition of sincere voting seems to cover all methods. "Preference" means pairwise preference. The definition applies to methods that ask for ratings, because if you rate X higher than Y, you're voting a preference for X over Y (in addition to actually expressing the ratings). If, in Point Ratings, you use that method as Approval, which is the best strategy for that method, and you vote a strategy that would be sincere in Approval, then that strategy is still sincere in Point Ratings. Mike Ossipoff _________________________________________________________________________ Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com. Share information about yourself, create your own public profile at http://profiles.msn.com.