[EM] pairwise matrices and ballots

[David Catchpole]

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
> ______________________________________________________
> Get Your Private, Free Email at http://www.hotmail.com
> 
> 

--------------------------------------------------------------------
Atheists aren't vagrants- but we have no invisible means of support.