[EM] thoughts on the pairwise matrix

Andrew Myers andru at cs.cornell.edu
Tue Nov 29 12:11:27 PST 2005

On Mon, Nov 28, 2005 at 06:41:34PM -0600, Paul Kislanko wrote:
> I don't have to support my argument, since I am asking for those who claim
> Condorcet methods are "better" to support the claim that those methods are
> "like" Nx(N-1)/2 different elections. They are not, unless I get to make
> Nx(N-1)/2 choices, which I don't get to do.

It seems we could easily generalize most Condorcet methods to allow the voter
to specify an NxN matrix instead of a sorted list. This would provide the same
information as the C(N,2) elections, with the added ability for a user to
provide an arbitrary preference graph that

 - violates transitivity
 - does not connect every pair of nodes,
 - or contains cycles.

Violations of transitivity and acylicity seem of dubious value to me, but they
could be accommodated.  So I'd claim that ranked ballots are just as good as
the hypothetical C(N,2) elections, if you can say that two candidates are
equally preferred on your ballot.

-- Andrew

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