Alex wrote: >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.
Well put, Alex (in both messages). If you want an example that sticks to the linear political spectrum, that can be done as well. To wit: 44% George > Al > Ralph 15% Al > George > Ralph 15% Al > Ralph > George 26% Ralph > Al > George Ralph loses in the first round, and Al beats George 56%-44% in the runoff. If 5% of the George > Al > Ralph voters switch to Ralph > George > Al, then Al loses in the first round and George wins the runoff 54%-46%. This example not only shows an simple case of non-monotonicity, but does it in the context of the classic right/left political spectrum. Moreover, if the George supporters have even approximate polling information, they know that they can get away with this voting trick with very little risk. It's quite realistic. There's a very large range of percentages where this exact example works. The only reason this sort of thing has not happened in Australia is because the third parties remain largely marginalized in their IRV elections. Which of course shows the other (perhaps more important, certainly more obvious) weakness of IRV: it does not break the system out of a two-party duopoly. -Adam
