1. Collect a set of ranked ballots

    2. 100 voters distribute their ballots in the following manner:
    12:a>d>c>b
    3:b>a>c>d
    25:b>c>a>d
    21:c>b>a>d
    12:d>a>b>c
    21:d>a>c>b
    6:d>b>a>c

  2. Based on a set of ranked ballots, compute the Pairwise Matrix

    3. The complete Pairwise Matrix is:

  3. Extract each of the defeats from the Pairwise Matrix

  4. Sort the defeats from strongest to weakest

    5. The sorted defeats are:
    A>D Strength:61 Margin:22
    B>A Strength:55 Margin:10
    A>C Strength:54 Margin:8
    C>B Strength:54 Margin:8
    D>C Strength:51 Margin:2
    D>B Strength:51 Margin:2

  5. Starting with the strongest defeat, consider each defeat in sequence with previously kept defeats, if any. If two or more defeats are equivalent, those defeats are considered together with previously kept defeats, if any. If any defeat under consideration, which has not yet been kept, is a part of a cycle, it is rejected. If any defeat under consideration, which has not yet been kept, is not a part of a cycle, it is kept.

    6. Consider the defeat A>D with our previously kept defeats
    No cycles are created, so it is kept and we consider B>A with our previously kept defeats
    No cycles are created, so it is kept and we consider A>C & C>B (since they are equivalent) with our previously kept defeats
    Both of these defeats are a part of a cycle, so they are rejected and we consider D>C & D>B (since they are equivalent) with our previously kept defeats
    Defeat D>B is a part of a cycle, so it is rejected. D>C is not a part of a cycle, so it is kept.

  6. The winner or winners will be those alternatives which were not defeated

    7. Since B remained undefeated, after all defeats have been considered, it wins.


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