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  1. Collect a set of ranked ballots

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

  3. Extract each of the defeats from the Pairwise Matrix

  4. For example, only if the number of people who preferred alternative A over B is greater then the number of people who preferred alternative B over A, can we say that A defeated B. The number of people who preferred A over B is the primary information we remember. We also keep the margin of the defeat, if it is needed. This margin is computed by subtracting the number of people who preferred B over A from those who preferred A over B.

  5. Sort the defeats from strongest to weakest

  6. If there are two or more pairwise defeats, each with equal strength, consider the margin of the defeat while sorting. The defeat with a greater margin is considered to be stronger. If two or more pairwise defeats have an equal strength and the margins are also equal, they are considered to be equivalent.

  7. 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.

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

Here are several, descriptive examples.



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