# [EM] pairwise matrices and ballots

MIKE OSSIPOFF nkklrp at hotmail.com
Fri Feb 25 20:26:58 PST 2000

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Blake--

You have in your possession Bruce Anderson's proof that
for every pairwise vote table there's a set of rankings that
produces that pairwise vote table.

It's in his paper entitled _How to Take Votes: New Ideas on
Better Ways to Determine the Winners_.

I at first thought it was obvious why that's true, but
now I realize that it isn't obvious. I'd thought that if
there's no limit on how many voters one can invent, then it
would be trivially easy to add people voting whatever the
table needs. Not as easy as I expected, since even a short ranking
says something about its candidates vs the ones it doesn't rank.

I haven't found rankings for the pairwise vote table that
you posted, but since Bruce said there's a ranking set for
every pairwise vote table, there surely is; that isn't something
that Bruce would be wrong about. Of course I'll try to find a
ranking set for the table that you posted.

> > 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?

Unless I'm mistaken, I have somewhere a paper by Brams & Fishburn
which used the word "MinMax" to describe a procedure that
considers every one of a candidate's pairwise comparisons,
rather than limiting itself to looking at his defeats.

I'll find my copy of that paper within a few days and will then
tell you where it's published.

Next time I'm at the nearest university library, I'll find for
you something there that uses "MinMax" in that way.

Your own use of "MinMax" for Plain Condorcet shows you that
that term is sometimes used for a method that considers only
a candidate's defeats when determining his score.

Mike Ossipoff
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