[EM] pairwise matrices and ballots

Blake Cretney bcretney at postmark.net
Thu Feb 24 19:32:03 PST 2000


> 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.

Blake Cretney

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