Alex and Adam gave three examples to try to show how IRV can violate monotonicity. Alex's second example was
>19% Bill > George > Ross >18% Bill > Ross > George >19% Ross > George > Bill >12% Ross > Bill > George >16% George > Bill > Ross >16% George > Ross > Bill > >Runoff is still Bill vs. George, and George wins. If 2% from the >Bill>George>Ross camp list their preference as Ross>Bill>George, the runoff >is Bill vs. Ross. Bill wins. But this isn't an example of nonmonotonicity. George wins, some voters uprank Ross, and then Bill wins. The upranking voters benefited from their insincerity, but monotonicity isn't violated in this example. To violate monotonicity, an example must cause a winner to lose by having some voters uprank him or cause a loser to win by having some voters downrank him. Alex's first Bill/George/Ross example and Adam's Al/George/Ralph example have the same problem. Here's a nonmonotonic IRV example taken from Philip Straffin's book Topics in the Theory of Voting: 6:A>B>C 2:B>A>C 4:B>C>A 5:C>A>B IRV gives the win to A, but if the B>A>C voters uprank A and vote A>B>C, then IRV gives the win to C. A went from winner to loser when some voters ranked him higher. ===== Rob LeGrand [EMAIL PROTECTED] http://www.aggies.org/honky98/ __________________________________________________ Do You Yahoo!? Yahoo! Greetings - send holiday greetings for Easter, Passover http://greetings.yahoo.com/
