Blake wrote: >the only realistic example wouldn't have people perfectly splitting the >vote, so it wouldn't prove that a result occurs only from vote >splitting, so it wouldn't prove anything at all.
Perhaps examples are too anecdotal. The case I made last night can be stated in terms of general principles rather than "look, for these particular numbers I can get this paradox." I should have done that. Let me now explain the origin of non-monotonicity in IRV with 3 candidates: Suppose A beats B, and B beats C (A vs. C is irrelevant for now). Non- monotonicity will occur under the following conditions: 1) B receives more first-choice votes than A, and A receives more first- choice votes than C. 2) In the count of first place votes, the difference between B and A is greater than the difference between A and C. 3) B's supporters are willing to gamble. Under those conditions, if some of B's supporters "defect" to C, they can promote C ahead of A, leading to a runoff between C and B. B now wins, only because he strategically sent some supporters away to another candidate. This paradox can occur with or without a Condorcet winner, since the A vs. C contest doesn't matter. The conditions are fairly general, so the monotonicity violation is hardly a special case. Alex
