[EM] question re: converting ballots into a matrix

[Paul Kislanko]

Before everybody jumps all over me again, it is possible to determine the
Borda WINNER from the pairwise matrix using the method Chris described. But
it is not possible to re-create the Borda scores from it. 

Nor is it possible to construct a pairwise matrix from just a list of the
Borda scores for all alternatives.

However, from a matrix that has alternatives as rows and rankings as
columns, it is possible to create a pairwise matrix and calculate Borda
scores. See, for instance, how I represent the computer rankings for college
football teams at http://football.kislanko.com/2005/bucklincomps.html (I
call it bucklincomps because you can use the same matrix to figure Bucklin
or Approval results).

> -----Original Message-----
> From: election-methods-bounces at electorama.com 
> [mailto:election-methods-bounces at electorama.com] On Behalf Of 
> Paul Kislanko
> Sent: Tuesday, December 06, 2005 11:24 PM
> To: 'Chris Benham'; 'rob brown'
> Cc: 'Kevin Venzke'; election-methods at electorama.com
> Subject: Re: [EM] question re: converting ballots into a matrix
> 
> I don't think Chris is right about this, unless the 
> definitions for "total
> votes for" and "total votes against" are defined in a way that isn't
> included in his description.
> 
> If "total votes for" is the sum of votes in the row 
> corresponding to the
> alternative, and "total votes against" is the sum of the 
> column, that gives
> an ordering "like" Borda's, but it does not give you the 
> Borda count, since
> there's no way to tell how many of the X>Y votes had X 2 
> spots higher than Y
> vs 1 spot higher than Y, and that distinction is necessary to 
> reconstruct
> the Borda count.
> 
> If the Borda count could be re-derived from the pairwise matrix, then
> Condorcet and Borda would have the same properties.
> 
> > -----Original Message-----
> > From: election-methods-bounces at electorama.com 
> > [mailto:election-methods-bounces at electorama.com] On Behalf Of 
> > Chris Benham
> > Sent: Tuesday, December 06, 2005 11:13 PM
> > To: rob brown
> > Cc: Kevin Venzke; election-methods at electorama.com
> > Subject: Re: [EM] question re: converting ballots into a matrix
> > 
> > 
> > 
> > rob brown wrote:
> > 
> > > I don't see how you can do something as simple as a borda 
> > count with 
> > > the data in a traditional matrix.
> > 
> > If you score each candidate  by [(total votes for)  minus  (total  
> > votes  against)]   then  you will  get  the equivalent
> > of  the  Borda scores (i.e. the candidate with the highest 
> > score will be 
> > the Borda winner, the candidate with the
> > second-highest score will be the Borda runner-up and so on.)
> > 
> > 
> > Chris  Benham
> > 
> > 
> > 
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