C>A=D>F
and add one to C in C vs. A, add one to C in C vs. D, etc. But when we see an "equal" such as A vs. D (as well as implied equals like B vs. E, etc), we just do nothing.
Has anyone ever considered also adding one-half a "point" to each of the equals? In other words, since A is ranked equal to D, add one-half to both A and D in the A vs. D pairwise match.
I know, at first blush, you might ask "why?". For determination of a Condorcet winner, it won't make a difference of course. I don't know how it will affect the various methods, but clearly some will be unaffected.
Still, I see various reasons why it seems more logically consistant to add the half point to each member of a tie. For one, it means you can easily calculate the number of ballots from the pairwise matrix, since each ballot will affect the matrix equally. For another, you can now do a borda count based on the matrix. The practical benefits of these two things, however, are secondary to just the logical consistancy.
So my question is: has this been discussed? (my guess: probably) Is there a reason for *not* doing it? Is there something I haven't thought through completely due to lack of coffee?
-rob
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