[EM] Richard & the diagram

[MIKE OSSIPOFF]

I'd written:

Richard has written about how one thing he likes about margins is
that it looks nice on a certain diagram.

Richard replies:

Not quite true. I described a diagram that I am using to visualize the
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.)


[...]

I reply:

Whatever. What you've written in that paragraph, and after that,
is something important to you. To each their own.

But when I talk to people about voting, they, believe it or not,
don't object to Plurality because distances from lines drawn on a
diagram aren't what they should be. No, what they say is that
people who prefer Nader should vote for Gore instead, because that's the
only way of making Bush lose.

You seem to regard this as some sort of mathematical game or art form
that should be above such mundane considerations as the concerns of
voters and the political and material consequences of the voting system.


Richard said:

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.

I reply:

I don't regard it that way, and it's an issue that never occurred to me.
As Demorep would agree, I'm not interested in setting anyone's votes
equal to anything different from what they were, though it's necessary
to disregard (drop) a defeat.

I regard as important the goal of getting rid of the lesser-of-2-evils
problem. That can be done while meeting Smith, ICC, Monotonicity &
Pareto.

Mike Ossipoff


[continuation of Richard's letter]:

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


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