[EMAIL PROTECTED]">Richard has written about how one thing he likes about margins isNot quite true. I described a diagram that I am using to visualize the
that it looks nice on a certain diagram.
differences between margins and winning votes. It has nothing to do
with aesthetics and everything to do with mathematical distances
(L1 distances in this case). The point of the diagram was only that
the contests with the least margins are closer to the "tie line" that
runs down the center. (Points to the left of the line are ignored
because they are represented by their mirror images to the right of
the line.)
If the AB contest has lesser margins that the CD contest, it is closer
to the tie line. Whenever a defeat is dropped in Condorcet completion,
it is as if we moved the associated point directly to the left until it
hits the tie line. That is equivalent to changing some number of win
votes to losing votes. The number of votes that would be changed by
this operation is equal to half the margin of victory. Another way of
looking at it is that a contest close to the tie line is more likely to fall
within the error margin ("noise"), so is in fact a "weak signal".
Ignoring such defeats is less likely to degrade the signal-to-noise
ratio.
(Alternate interpretations: Instead of moving horizontally, you can
move down and to the left on a 60 degree slope until you hit the
tie line, equivalent to changing ties to losing votes, or you can move
up and to the left, equivalent to changing winning votes to ties.
These alternate interpretations do not change the resulting L1
distance, however.)
If the CD contest has more winning votes, but lesser margins, than
the AB contest, it is closer to the apex of the diagram (representing
100% tie votes), but farther from the tie line. If you interpret
dropping a defeat as equivalent to setting all votes in that contest to
ties, then winning votes is a better criterion. I don't share that
interpretation, however.
Richard
