[EM] Default MMV meaning, for MMV without qualifying designations

Markus Schulze markus.schulze at alumni.tu-berlin.de
Wed Dec 11 13:10:40 PST 2013

Dear Mike Ossipoff,

you wrote:

 > How would Beatpath deal with equally strong beatpaths between
 > two alternatives? If CSSD encounters two equally weakest
 > defeats in the current Schwartz set, does it drop both together?

There is an important difference between Tideman's ranked pairs
method and the Schulze method:

    Suppose that there are q defeats of equal strength. Then to
    calculate all potential winners of the ranked pairs method,
    the q! possible ways to consider one of these defeats after
    the other have to be considered separately. When q is large,
    this calculation can be quite cumbersome. Therefore, "greedy
    algorithms" have been proposed that are intended to find a
    subset of the set of potential winners in a polynomial runtime.

    On the other side, all potential winners of the Schulze method
    can be calculated in a runtime O(C^3), where C is the number
    of candidates. Even when there are many defeats of equal
    strength, the runtime to calculate all potential winners
    is O(C^3). Therefore, there is no need to find a "greedy
    algorithm" for the Schulze method.

Markus Schulze

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