On May 13, 2010, at 10:08 PM, Dave Ketchum wrote:
I read of arranging ballot data in a triangle, rather than in a matrix as usually described. A minor detail, but what would be easiest for ballot counters is most important while they count, though rearranging for later processing would be possible.
in all cases, i am assuming that a computer is tabulating the ballots. to count Condorcet by hand is difficult, because (if number of candidates is N) you would have to update up to N*(N-1)/2 numbers out of N*(N-1) for each ballot handled, rather than 1 of N numbers as is done for FPTP (the latter lets you sort to piles for quick double checking).
the reason i prefer that triangle (which is just like the NxN matrix with half of the elements folded over the main diagonal and also sorted in order of the Condorcet ranking (assuming no cycles, if there are cycles, even one not including the CW, the triangle won't look so pretty) is because it displays the result in such a way that you can immediately infer the who-beats-who results from it. even though i haven't seen it anywhere else before, i make no claim to novelty. i really just can't understand why anyone would use the NxN square matrix. it's really hard to glance at it and see what numbers to pair together.
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