[EM] number of possible ranked ballots given N candidates

[rob brown]

On 12/14/05, Paul Kislanko <kislanko at airmail.net> wrote:
>
> I don't have a philosophical objection to using the pairwise matrix on the
> counting side of the system at all. I just think when comparing different
> Condorcet methods it would be helpful to have the original voters' ballots,
> because when we get into hypotheticals like "if x B>A voters had changed to
> B>C>A then..." we'd have the data on how likely that might be.
>

If that is the case than I must apologize as I completely misunderstood you
in our earlier discussion/debate.  I had understood that you didn't want any
method to use the matrix, even as an intermediate step.

I do wonder if there is a middle ground.  I mentioned previously the idea
that, in addition to the pairwise matrix (and number of ballots, which the
matrix does not store), if we had an additional matrix that represented
"similarity" of candidates.  Certain candidates tend to be liked or disliked
by the same subset of voters, and it would be interesting if the ballots
could be processed into such a correllation matrix that measured this factor
for each candidate pair.  Each candidate pair might have a number which
represented the percentage of pairwise agreements....that is, if both A and
B are ranked higher (or lower) than C on a ballot, that would count as an
agreement, and would increase the percentage in the A-B slot.

If you had this in addition to the pairwise matrix, I bet you could do a
much more accurate "deconstruction"  or expansion into ballots.  It would
still be an approximation, but possibly a much better one.

I doubt there is anything useful you could do with this data in the actual
calculation of the winner, but it is certainly interesting data nonetheless.
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