[EM] number of possible ranked ballots given N candidates

Rob LeGrand honky1998 at yahoo.com
Wed Dec 14 15:37:01 PST 2005

```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/

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