[EM] A small remark about the Schulze-method

[Peter Barath]

As far as I can understand, diferent places tell us
about the Schulze-method like:

1. A candidate "path-beats" another one, if
its best beatpath to the other is the better. The
Schulze-winners are the "un-path-beaten" ones.

or, which gives the same result:

2. Calculate the Schwartz set, drop the outsiders.
Then drop the weakest defeat. Do this while possible,
and the remainders are the Schulze-winners.

I think maybe we should add an instruction: If there
are more than one Schulze-winners, do the whole thing
again with only them.

Example:

ABCD
BCDA
BACD
CDAB
DACB

Here A beats B and C, B beats C and D, D beats A.
These are all 3:2 beats. And C beats D by 4:1.

Since  A > B > C > D > A  there are beat-paths from
each one to each other one. And only C > D is stronger,
all other ones are the same. So A, B, C are all
"un-path-beaten", or, if you like it, in the first
step, A,B,C,D are all in the Schwartz set, then
dropping all weak defeats, only C > D defeat remains.

So, A, B, C are the Schulze-winners.

But A can rightfully say that itself alone must be
declared as a winner, because it is a Condorcet winner
among A, B, C.

It is a very unlikely scenario, I admit.

Peter Barath

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