# [EM] number of possible ranked ballots given N candidates

Paul Kislanko kislanko at airmail.net
Wed Dec 14 16:02:33 PST 2005

```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: election-methods-bounces at electorama.com
> [mailto:election-methods-bounces at electorama.com] 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
> rob at approvalvoting.org
> 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
>

```

More information about the Election-Methods mailing list