Hi folks,
Some people have asked me why my cardinal pairwise method only looks at
the winning ratings differentials, rather than the margin of
winning-losing ratings differentials. My reply is that the winning ratings
differentials (WRD) approach is what makes cardinal pairwise so danged
strategy-resistant. Here's a quick example which I hope helps to
illustrate the difference between the two methods with respect to
strategic vulnerability.
K>D>>B is a shorthand for something like K 100 > D 100 > B 0. Or K>D>B
with an approval cutoff between D and B. Or you could imagine that
something like 19: K>D>>B ; 5: K>>D>B is a summary of the K>D>B voters,
approximating a complex set of ratings information into a simple 19:5
ratio. Anyway, here's the example.
3 candidates: Kerry, Dean, and Bush. 100 voters.
Sincere preferences
19: K>D>>B
5: K>>D>B
4: K>>B>D
18: D>K>>B
5: D>>K>B
1: D>>B>K
25: B>>K>D
23: B>>D>K
Kerry is a Condorcet winner.
Altered preferences
19: K>D>>B
5: K>>D>B
4: K>>B>D
18: D>K>>B
5: D>>K>B
1: D>>B>K
21: B>>K>D
23: B>>D>K
4: B>D>>K (these are sincerely B>>K>D)
There is a cycle now, K>B>D>K
For each defeat, here are the winning and losing strong preferences, and
the winning-losing margin
D>K : 10-9 = +1
K>B : 46-48 = -2
B>D : 44-43 = +1
If we are using marginal ratings differentials, then the Bush voters'
strategy succeeds, and Bush wins. This is what I call a flagrant strategic
incursion. Using winning ratings differentials, there is no way for Bush's
supporters to get him elected.
Sincerely,
James
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