[EM] Condorcet cyclic drop rule

[Tom Ruen]

Okay, I understand the dropping rule: We look at how many voters supported
each victory, and eliminate the smallest victory of a cycle.

Let me repeat my examples:

#1 Example ballots: AC=5, BA=4, CB=3

 Pair elections:
A:B=5:7   B/A (7) - weakest
B:C=4:8   C/B (8)
A:C=9:3   A/C (9)

 Dropping B/A counteracts only 7 voters' preference, compared with 8 or 9.
The result is A>C>B, and A wins.

 However if some "A" voters bullet vote:
#2 Example ballots: AC=3, A=2, BA=4, CB=3

 Pair elections:
A:B=5:7  B/A (7)
B:C=4:6  C/B (6) - weakest
A:C=9:3  A/C (9)

Dropping C/B counteracts 6 voters' preference, compared with 7 or 9.
The result is B>A>C, and B wins.

It is strange - A supporters might dislike B and C equally, but strategic
voting for C second helps while A loses if supporters bullet vote instead!

Ranking is truly a bizarre world!

Random determination to break a cycle would seem a safer bet to me to
discourage insincere voting in lower rankings.

I would guess cycles come from three types of sources:
1. Irrationally or thoughtlessly lower ranking.
2. Insincere strategic lower rankings.
3. Voters in different coalitions may use different fundamental criteria for
judging candidate. (Imagine 3 candidates {A,B,C} and 3 qualities/issues
{X,Y,Z}. Each candidate has a different set of 2 of the 3 qualities - A has
X much and Y some, B has Y much and Z some, C has Z much and X some. Then
voter come in 3 groups: one likes Y much and X some (vote AB?); one likes Z
much and Y some (vote BC?); one likes X much and Z some (vote CA?). This
could cause a ranking cycle if no coalition group has a majority.)

Tom Ruen

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*** Mike said:

...
There are at least 2 additional ways:

3. Defeat support (number of voters voting for that defeat)
4. Defeat opposition (number of voters voting against that defeat).

Markus, Steve Eppley, Norm Petry, Rob Lanphier & I all prefer
defeat support as the measure of a defeat's strength.

That's largely because that measure of defeat strength confers some
important strategy criterion compliances.

It's also because defeat support is what is important tothe
lesser-of-2-evils voter. He's willing to do whatetever it takes to reliably
& effectively vote against his greater evil.

It's also because it's the measure that minimizes the number of
overruled voters. A voter is overruled if he's voted for one of the
winner's defeats (doubly overruled if he's voted for 2 of the winner's
defeats, etc).

Defeat Support is what Condorcet himself specified. Norm & Markus
posted quotations about that. They're in the archives for last year.

Now, if we didn't care about overruled voters, lesser-of-2-evils
problem, etc., then margins would be good. Margins is better than
ratio. Margins combines ratio & turnout. Two defeats have the same
ratio but one has a bigger turnout. The bigger turnout gives that
defeat more validity, and that defeat has a bigger margin.

Mike Ossipoff