[EM] Example with tie in Schulze method but not in IRV

Kristofer Munsterhjelm km_elmet at t-online.de
Wed Sep 14 01:29:33 PDT 2016

On 09/14/2016 09:57 AM, Luděk Belán wrote:
> Chris,
> thank you for confirmation. Do you know any variant of Schulze method
> (or of other Condorcet method) to determine the winner in this example?
> Thank you.

The Condorcet matrix is (row defeating column)

- A B C
A - 3 2
B 2 - 3
C 3 2 -

So the candidates are completely indistinguishable from the pairwise
matrix alone. No method that uses only the pairwise data can tell the
candidates apart.

I think you have three options:

a. Use a random tiebreak (MAM at http://mam.hostei.com/default.php does
that for your ballot set).
b. Accept the tie.
c. Use a Condorcet method that use more than just the pairwise data
(e.g. Condorcet-IRV hybrids like Woodall), or break the tie with a
non-Condorcet method.

For your ballots, every candidate is part of the Smith set. If you break
the tie with IRV, A wins. If you break the tie with Bucklin, C wins.

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