On May 20, 2004, at 6:03 PM, MIKE OSSIPOFF wrote:
Here's a conceptual example that I think better illustrates the problem
that I observed. Suppose you vote in an election in which there are 6
candidates and you have no idea how anyone else votes. Your sincere CR
profile for candidates A ... F is
SincereCR: A(0.7), B(0.5), C(0.3), D(0.1), E(-0.1), F(-0.3)
(This assumes signed CR's, with an approval cutoff of zero.) What I call
"ExaggerateCR" simply applies a linear transformation so that the max
and min CR's are +1 and -1:
I reply:
If you do anything other than mutliplying all of a particular voter's ratings by the same factor, then you'll get something that's meaningless.
I think the operation being applied to each rating of a voter is f(r) = m * r + b
By choosing m and b for voter, the highest rating scales to 1.0, the lowest to -1.0 and everything else proportionally in between.
And if you multiply different voter's ratings by different factors, then you don't have a valid CR count. Not that you're necessarily doing a CR count.
It's not straight-CR, but it's still useful. I'd say it makes sure everyone has the same voting strategy for CR, which adds a measure of fairness. This particular variation can still be taken advantage of. The proper vote is 1.0 for all choices with positive utility and -1.0 for all others. That maximizes my expected utility. But, the experiment as I understand it was applying various voting systems to honest preferences.
Brian Olson http://bolson.org/
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