[EM] Steph's Condorcet example

[MIKE OSSIPOFF]

There was a question about Condorcet returning a tie in this
example:

Input matrix
0 23 25 65
24 0 11 87
44 55 0 22
33 11 44 0

Initial defeats matrix:
0 0 0 65
24 0 0 87
44 55 0 0
0 0 44 0

When defeat-strengths are measured by winning votes:

  When we deal with equal defeats by comparing their margins:
    BeatpathWinner/CSSD chooses A
    Ranked-Pairs chooses C

  When we treat equal defeats as equal, instead of looking at margins:
    BeatpathWinner/CSSD chooses A & C
    Ranked-Pairs chooses C.


When Ranked-Pairs encounters 2 or more equally strongest unconsidered
defeats, and either we simply call those defeats equal, or
when we compare margins, they're equal too, I've proposed a way
for RP to deal with those equally strongest unconsidered defeats:

Call them the "tie-defeats". A tie defeat is "qualified" if it
isn't in a cycle consisting only of itself and some kept defeats.

Keep a qualified tie defeat if it isn't in a cycle consisting only
of itself and some combination of kept defeats and qualified defeats.

Mike Ossipoff




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