[EM] pairwise matrices and ballots
bcretney at postmark.net
Thu Feb 24 19:32:03 PST 2000
MIKE OSSIPOFF wrote:
> 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.
I don't know where you got that idea. Try the following example:
A B C
A X 1 3
B 2 X 1
C 1 3 X
> 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.
Could you please quote the sources you used for your definition of
Simposon-Kramer, and the different uses of MinMax? Make sure that they were
actually considering the issue of incomplete rankings.
> 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.
Please illustrate this with an example. I don't understand what you mean.
> For that reason I
> avoid using the name "MinMax", since it is used with more than
> 1 meaning.
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