Bolson--
I'd said:
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.
You replied:
I think the operation being applied to each rating of a voter is f(r) = m * r + b
That's what I assumed was meant too, the application of the same linear function to all of the numbers.
You continued:
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.
I reply:
No, not at all. Yes, the constants of the linear function can be chosen to give 1 and -1 for the extreme values of the linear function, and yes the output will all be between 1 and -1. But no, the numbers will not remain in proportion to the input numbers. Take 2 numbers of different value. Multiply them by the same "m", and yes they're proportional to the original numbers. So far so good. But now you add "b" to all of them. Whoops! No more proportional!
You continued:
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.
I reply:
What? It makes sure everyone has the same voting strategy for CR? Could you reword that? You said it isn't CR. You mean that it makes sure that everyone votes the same strategy in something that's similar to CR? How does it make sure that everyone votes the same strategy? You say it causes everyone to vote the extremes. That sounds like CR strategy. What desirable properties does the method that you're talking about have?
You continued:
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.
I reply:
Positive and negative utility? Ok, that's different from the strategy of CR & Approval.
But would you mind deriving your strategy for us? Why exactly should someone give 1 to candidates with positive utility and -1 to candidates with negative utility? You don't do that in CR or Approval. Why would you do it with the method that you're talking about?
You continued:
That maximizes my expected utility.
That's what I ask you to demonstrate.
You continued:
But, the experiment as I understand it was applying various voting systems to honest preferences.
I reply:
If we assume honest ratings, then ordinary CR counting, just adding up each candidate's ratings, is what maximizes SU.
Mike Ossipoff
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