Defend the statement that "Condorcet looks at ALL that the voters say". No
method that begins counting from a pairwise matrix can do that. Furthermore,
there are numerous "Condorcet" methods because there are numerous ways to
distinguish between the cycles created when ONLY the pairwise matrix is
used.
If I may jump in -- I have to take issue that Condorcet "doesn't look at all the voters have to say" because it "begins counting" with the pairwise matrix.
It begins counting with the ballots. By the time it gets to the pairwise matrix, it has certainly eliminated a lot of data, having distilled possibly several megabytes of data into a few kilobytes or less (depending on how many candidates and how many ballots). But then, it has to distill it further, into maybe a single byte of data (assuming there are less than 256 candidates).
Somewhere along the line, information has to be pared down and eliminated. The pairwise matrix is an intermediate step between having several megs (all the ballots) and 1 byte (a winner). I'm not sure I understand why having an intermediate step is such a problem.
-rob
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