Rob LeGrand is correct. You can't derive the pairwise matrix solely from a matrix that only records the counts for each rank.
I think it is possible, though, to use the combination of pairwise matrix and the counts-by-rank matrix together to retrieve the the original ballot preferences. > -----Original Message----- > From: [EMAIL PROTECTED] > [mailto:[EMAIL PROTECTED] On Behalf Of > Rob LeGrand > Sent: Wednesday, December 14, 2005 5:37 PM > To: Election Methods Mailing List > Subject: Re: [EM] number of possible ranked ballots given N candidates > > Paul Kislanko wrote: > > Yes. The pairwise matrix plus this "how many voters ranked > A at rank R" > > could be combined to give more information. In fact, the pairwise > > matrix can be derived as easily from the "how many voters > ranked A at > > rank R", but not vice-versa. > > I don't believe that's true. The two ballot sets > > 3:A>B>C > 2:B>C>A > 2:C>A>B > > and > > 2:A>B>C > 1:A>C>B > 1:B>A>C > 1:B>C>A > 1:C>A>B > 1:C>B>A > > result in different pairwise matrices (no Condorcet winner in > the first, > A is CW in the second), but they both have the same rank profile: > > A is first on 3 ballots, second on 2 ballots, third on 2 ballots > B is first on 2 ballots, second on 3 ballots, third on 2 ballots > C is first on 2 ballots, second on 2 ballots, third on 3 ballots > > -- > Rob LeGrand, psephologist > [EMAIL PROTECTED] > Citizens for Approval Voting > http://www.approvalvoting.org/ > > __________________________________________________ > Do You Yahoo!? > Tired of spam? Yahoo! Mail has the best spam protection around > http://mail.yahoo.com > ---- > election-methods mailing list - see http://electorama.com/em > for list info > ---- election-methods mailing list - see http://electorama.com/em for list info
