# [EM] pairwise matrices and ballots

David Catchpole s349436 at student.uq.edu.au
Sat Feb 26 21:05:12 PST 2000

```Ohhh! I am now less confused. Thanks Blake.

On Sun, 27 Feb 2000, Blake Cretney wrote:

> 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_.
>
> Referring to page 184 (E-1) of his paper, he states:
>
> > Theorem:  Given any round robin results array, there exists a set of
> voter's preference
> > over the alternatives involved whose corresponding pairwise matches produce
> that array.
>
> He then goes on to prove that result.  However, you have
> misinterpreted what he means by a "round robin results array".  Check
> his definition on p 80 (VI-32).  It is clear that a round robin array
> only includes the information of wins, losses, and ties.
>
> > r(X,Y)=1 if and only if X won its match against Y,
>
> ----------
> > > > 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.
> >
> > I didn't say they were considering the issue of incomplete
> > rankings. Or if I seemed to say that, I didn't mean to.
> >
> > I don't know of a MinMax or Condorcet definition in an academic
> > article that says anything about incomplete rankings.
>
> That's what I thought.  My point is, that if they aren't considering the
> issue of incomplete rankings, they might say one of:
>
> 1.  Find the candidate who has the fewest votes against it in any pairwise
> contest.
> 2.  Find the candidate who has the fewest votes against it in its greatest
> loss.
> 3.  Find the candidate who has the smallest margin of defeat in its greatest
> loss.
>
> Knowing that all three are equivalent for their purposes.  If you take their
> words out of that context, and instead apply them to incomplete rankings, you
> have them arguing for a method that they likely never even considered, let
>
> Note, the following is from a different posting by Mike Ossipoff, on the same
> subject:
> > 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.
>
> True, but I'm still interested to know if it was used this way in any
> published journal, where the issue of incomplete rankings was considered.  As
> for my use, I find it very convenient to use the term Minmax for the basic
> algorithm, and then specify separately, usually in brackets, which method I am
> using to measure pairwise contests.  This seems simpler than having three
> separate names for the three suggested ways of doing this.
>
> As well, I dislike the term "Plain Condorcet" for the following reasons:
>
> 1.  It is unknown off this list.
> 2.  It implies that Condorcet invented this method.  This does not appear to
> be the case, although his words may have been taken out of context, as I
> described above.
> 3.  It is confusing because one would think that the Condorcet winner would
> be identical to the winner of Plain Condorcet.
>
> ---
> Blake Cretney
>
>

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