In one discussion, where I advocated a more "grokkable" output format, I argued that the pairwise matrix is effectively raw data....that is, it is the input data prior to processing and therefore not the best thing to show when presenting results.
In another, where Paul K indicated a dislike for methods that use the pairwise matrix because they throw away lots of data prior to doing any processing, I suggested that the matrix is *not* raw data, but data after some processing has already happened, so in my opinion the complaint is unjustified.
What do you consider it?
Another question about the matrix.....what kind of information is lost when going from ballots to the matrix? Obviously a lot of information is thrown away. My question is: 1) what interesting things are in this "lost data", and 2) is there anything in that data that maybe *should* be involved in determining the winner?
For 1, I'm thinking that "similarity" between candidates is lost. For instance, the ballots might show that people who rank C high, also tend to rank F high. This seems to be irrecoverably lost when going from ballots to matrix (right?). An interesting exercise might be to construct a "similarity matrix" that could display this information to those who are interested. Is there anything else of interest in the ballots that is lost by the time it is compressed into a matrix?
For 2, I can't come up with anything that is in this data that should be used to determine the winner. Similarity, while interesting, doesn't seem to have any relevance to picking a winner. But that's just my first thought, so I'd be interested in what others think.
-rob
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