[EM] question re: converting ballots into a matrix

[rob brown]

When putting ballots into a pairwise matrix, we take a ballot like this:

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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