[EM] pairwise matrices and ballots

David Catchpole s349436 at student.uq.edu.au
Sat Feb 26 13:53:46 PST 2000

I'm not quite sure of what you mean, but, for instance, there's no way to
produce rankings such that |{A>>B}|=|{B>>C}|=|{C>>A}|=total all
votes. Could someone clarify?

On Sat, 26 Feb 2000, MIKE OSSIPOFF wrote:

> 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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