Mr. Schulze wrote in part- Blake Cretney demonstrated in his 3 Nov 1998 mail that monotonicity is violated when one simply re-applies this algorithm (http://groups.yahoo.com/group/election-methods-list/message/1955). Example 1: 3 voters vote A > B > C > D. 2 voters vote D > A > B > C. 2 voters vote D > B > C > A. 2 voters vote C > B > D > A. The pairwise matrix looks as follows: A:B=5:4 A:C=5:4 A:D=3:6 B:C=7:2 B:D=5:4 C:D=5:4 B and D are SSD winners. When SSD is re-applied among candidate B and candidate D, then candidate B wins decisively. Example 2: One voter changes from D > A > B > C to A > D > B > C 3 voters vote A > B > C > D. 1 voter votes D > A > B > C. 1 voter votes A > D > B > C. 2 voters vote D > B > C > A. 2 voters vote C > B > D > A. The pairwise matrix looks as follows: A:B=5:4 A:C=5:4 A:D=4:5 B:C=7:2 B:D=5:4 C:D=5:4 A, B, and D are SSD winners. When SSD is re-applied among candidate A, B, and D then no further reduction of the winner-set can be achieved. Therefore, Random Ballot is used so that candidate D wins with a probability of 1/3. This can be interpreted as a violation of monotonicity. --------- D- I note again that changing votes is a very major election felony. I note that if there are 1 or a few *changed* ballots (with the other ballots staying the same), then there can be *changed* results. Hardly a surprise --- since changing starting conditions routinely can change the results -- commonly called the *scientific method*. Basic point-- the election method being used operates on the votes cast (not a zillion repeat elections having the same choices and the same voters). When there is only a 1 vote difference in head to head results, then there should be no surprise if 1 voter changes his/her ballot ---- as if such voter (only) suddenly detected the results of all the other *secret* ballots (through criminal knowledge) and then changes his/her ballot to maximize *his/her* power in affecting the results -- depending on the method being used. In other words, a whole lot of the criteria floating around are quite criminal --- (ballots changed- changed results, ballots removed- changed results, ballots added- changed results). Also, in the above 2 examples --- Which of the choices get a majority of YES votes ??? Which group of voters is the *true* majority (or *true* minority) ???
