In my demonstration that PC is nonfalsifying, I said:
In PC, X has a majority defeat, and the CW never has a majority defeat, and so X can't win in PC, since it always has a stronger defeat than the CW does. [end of quote] Of course it isn't true that the CW never has a majority defeat, if someone order-reverses against him. Here's what I should have said: Because a majority prefer the CW to X, and vote the CW over him, X has a majority defeat. For any candidate Z, other than the CW, a majority of the voters prefer the CW to him, and so they rank the CW, but not Z (because I said that everyone ranks down to the CW, but no lower). That means that a majority of the voters don't rank Z. That means that Z doesn't beat anyone by majority. So only the CW beats other candidates by majority. So, when the X>CW voters order-reversed by voting Y over the CW, they removed the only majority defeat that Y could have. Y now has no majority defeat. X has a majority defeat. Y doesn't. X can't win in PC. So order-reversal doesn't benefit anyone; it can't elect someone whom the reversers prefer to the existing winner, the CW. As I said before, if reversal won't do it, truncation won't either, since, compared to reversal, it merely weakens a defeat of the sincere CW. In the case of PC, the truncation means that now there are 2 candidates without majority defeat instead of just 1--Y and the CW. In the case of BeatpathWinner, the CW's submajority defeat is another reason why X can't have a majority beatpath to the CW. In the case of RP & SSD, the CW's submajority defeat is one more reason why his defeat of X can't be the weakest defeat in a cycle. So no one benefits by order-reversal or truncation. Obviously no one benefits by extending their ranking past the existing winner, to people whom he likes less than the existing winner. So no one benefits by a strategy change. Mike Ossipoff _________________________________________________________________ Send and receive Hotmail on your mobile device: http://mobile.msn.com
