[EM] pairwise matrices and ballots

[MIKE OSSIPOFF]

Blake wrote:


>
>Often people want to create examples involving pairwise methods,
>usually to show that the method behaves badly in some situation.
>Since not all pairwise matrices are possible, it is customary to
>provide a set of ballots instead of just providing a pairwise matrix.

For any pairwise preference matrix, it's possible to devise
a set of rankings that will give that pairwise preference matrix.
So, for pairwise methods, it's unnecessary to furnish rankings
for an example--the pairwise preference table is sufficient.

***

By the way, MinMax is sometimes used to mean what we here call
Plain Condorcet, and is sometimes used to mean Simpson-Kramer--
two different methods. And they're still different methods even
if Simpson-Kramer counts votes-against in pairwise comparisons.
The difference is that Simpson-Kramer looks at all pairwise
comparisons, not just at pairwise defeats. For that reason I
avoid using the name "MinMax", since it is used with more than
1 meaning.

Mike Ossipoff


Mike Ossipoff



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