<html><head></head><body>MIKE OSSIPOFF wrote:<br>
<blockquote type="cite" cite="mid:F196AkwtsQztQoPAzda000008a0@hotmail.com">Richard has written about how one thing he likes about margins is
<br>
that it looks nice on a certain diagram. </blockquote>
Not quite true. I described a diagram that I am using to visualize the<br>
differences between margins and winning votes. It has nothing to do<br>
with aesthetics and everything to do with mathematical distances<br>
(L1 distances in this case). The point of the diagram was only that<br>
the contests with the least margins are closer to the "tie line" that<br>
runs down the center. (Points to the left of the line are ignored<br>
because they are represented by their mirror images to the right of<br>
the line.)<br>
<br>
If the AB contest has lesser margins that the CD contest, it is closer<br>
to the tie line. Whenever a defeat is dropped in Condorcet completion,<br>
it is as if we moved the associated point directly to the left until it<br>
hits the tie line. That is equivalent to changing some number of win<br>
votes to losing votes. The number of votes that would be changed by<br>
this operation is equal to half the margin of victory. Another way of<br>
looking at it is that a contest close to the tie line is more likely to fall<br>
within the error margin ("noise"), so is in fact a "weak signal".<br>
Ignoring such defeats is less likely to degrade the signal-to-noise<br>
ratio.<br>
<br>
(Alternate interpretations: Instead of moving horizontally, you can<br>
move down and to the left on a 60 degree slope until you hit the<br>
tie line, equivalent to changing ties to losing votes, or you can move<br>
up and to the left, equivalent to changing winning votes to ties.<br>
These alternate interpretations do not change the resulting L1<br>
distance, however.)<br>
<br>
If the CD contest has more winning votes, but lesser margins, than<br>
the AB contest, it is closer to the apex of the diagram (representing<br>
100% tie votes), but farther from the tie line. If you interpret<br>
dropping a defeat as equivalent to setting all votes in that contest to<br>
ties, then winning votes is a better criterion. I don't share that<br>
interpretation, however.<br>
<br>
Richard<br>
<br>
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