# [EM] "scored condorcet", etc

Gervase Lam gervase.lam at group.force9.co.uk
Tue Nov 22 16:06:35 PST 2005

```On Mon, 2005-11-21 at 16:00 -0600, Paul Kislanko wrote:
> I have a personal distrust of methods that "score" by looking at only the
> contents of the pairwise matrix, but there should surely be a mapping from
> the CW back to the ballots that contributed to the CW being the CW. Take
> those ballots and remove all winners, moving up all alternatives ranked
> lower than the winner. Then form a new pairwise matrix from the revised
> ballots, etc.

Suppose there are candidates A, B, C and D.  B is the Condorcet winner
and has the following pairwise results:

45-5  B:A
37-13 B:C
29-21 B:D

Now, the B v. D result is the pivotal result as it is the closest result
of the three.  Therefore, it is the most critical one in contributing B
to be the Condorcet Winner (I hope I got the gist of your post correct
here).  So, let's convert the results to margins:

+40 B:A
+24 B:C
+8  B:D

Now, it could be argued that we are heading towards a MinMax(Margins)
type method here.  And MinMax methods look directly at the pairwise
matrix.

Carrying this further, we then need to remove the ballots that
contributed to B being the Condorcet Winner.  That is, of the ballots
that ranked B>D, 8 need to be removed (or 9, depending on your point of
view).  But which 8 (or 9)?  That is at best non-trivial.

Thinking more about the "mapping" idea, the pairwise matrix is really
only a way of "mapping" ballots into a convenient form so as to
determine an election result.  I don't think somebody throwing a load of
ballots at me and them asking me to give a result "just like that" is
reasonable.  That is unless the person doesn't mind me using the Random
Ballot method.

The only alternative "mappings" I can think of are methods that are
Condorcet compliant.  Is Borda a Condorcet compliant method?  From my
vague recollections, I think there are other methods that are Condorcet
compliant but don't use a pairwise matrix.

Thanks,
Gervase.

```