Dear Rob, you wrote (4 Oct 2001): > Is it possible for a method based purely on ranked ballots to be both > clone-independent and nonmonotonic? In particular, can anyone come up > with an IRV example that violates independence of clones? I don't > remember having seen one.
When there are no ties (for candidate with fewest number of actual first preferences), then IRV is clone-independent. Whether IRV is clone-independent in the case of ties depends on the used tiebreaker. Example 3 voters vote A > B > C. 2 voters vote B > C > A. 1 voter votes C > B > A. Step 1: A has 3 votes; B has 2 votes; C has one vote. Step 2: C is eliminated. A has 3 votes; B has 3 votes. Most IRV supporters suggest that when there is a tie then that candidate should be eliminated who had fewer votes in the latest step; this means that in the example above --as candidate A had 3 votes in the first step while candidate B had only 2 votes in the first step-- candidate A wins decisively so that clone-independence is violated. However, with a random tiebreaker IRV is clone-independent even when there are ties. ****** Another example for a nonmonotonic clone-independent election method is Pairwise-Elimination: http://www.fortunecity.com/meltingpot/harrow/124/methods.html As far as I know, this election method is also called "Arrow-Raynaud Method." But I am not sure about that. Markus Schulze