[EM] number of possible ranked ballots given N candidates

[Paul Kislanko]

Just a thought for your endeavor. A way to save "more" information than the
pairwise matrix but less than saving counts of each ballot configuration is
to save an NxN matrix with column headings being count of #1, #2, ... #N
ranks and rows being the Alternatives. Use the rule:
 
If equals are found, assign the next alternative rank (r+1) where where r is
the rank the previous alternative listed would've had if there were no
equals. I.e. ranks are assigned 1,1,3 for A=B>C. 
 
This takes no more space than the pairwise matrix, but contains much more
information. See http://football.kislanko.com/2005/bucklincomps.html for an
example with 119 alternatives and any number of voters.

 

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