[EM] question re: converting ballots into a matrix

[Paul Kislanko]

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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