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: [EMAIL PROTECTED] > [mailto:[EMAIL PROTECTED] On Behalf Of > Chris Benham > Sent: Tuesday, December 06, 2005 11:13 PM > To: rob brown > Cc: Kevin Venzke; [email protected] > 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 > > > > ---- > election-methods mailing list - see http://electorama.com/em > for list info > ---- election-methods mailing list - see http://electorama.com/em for list info
