Chris Benham has been trying to explain this to me in an offline discussion, but I still don't get it. Suppose my preference ranking (inferred from my "sincere" CR ratings) is A > B > C. Naturally, I should strategically give A the highest possible rating and C the lowest. If I know A will beat C, I should give B the lowest rating to ensure that A wins over B. If I know C will beat A, I should rate B highest so that C does not win over B. But if I don't know which of A or C will come out ahead, my strategy options are more complicated. If I give B a low rating, this increases A's chance of winning, but it also increases C's chance of winning. If I raise B's rating to shut out C, I also run the risk that A will lose. It's not clear to me that the best compromise strategy wouldn't be to give B an intermediate rating somewhere between A and C.Message: 3 Date: Wed, 25 Feb 2004 01:15:41 +0000 From: "MIKE OSSIPOFF" <[EMAIL PROTECTED]> Subject: [EM] There's nothing wrong with Average Rating.
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CR is strategically equiovalent to Approval: In CR, you maximize your expectation by giving maximum points to those candidates for whom you'd vote in Approval, and giving minimum points to the rest.
That's one reason why CR isn't emphasized much here, because it's strategically equivalent to the simpler Approval method.
In my view, strategy is basically a game of judging probabilities and weighing tradeoffs. If you were to formulate the objective of voting strategy mathematically (has anyone done this?), you would probably find that for the above case the optimum strategy can be defined in terms of a function giving your optimum B rating as a function of your sincere candidate ratings and your estimated probability distributions for the aggregate group ratings. Whatever the form of this function, my guess is that it would be continuous. (For simplicity, I assume rating levels are not discretized.) Furthermore, the function range covers the high and low rating limits (as demonstrated above), so for any intermediate rating level there will be some condition under which your optimum B rating is at that level, implying that CR is not strategically equivalent to Approval.
On the other hand, it may be that the optimum-rating function looks more and more like a discontinuity as the number of voters increases, so I could be wrong - maybe CR does reduce effectively to Approval for large voting populations. I don't know. Furthermore, if the optimum CR strategy is so horrendously complicated that it can't be stated in plain English terms that the average voter can understand, that alone may be sufficient grounds for eschewing CR in favor of Approval.
Comments?
Ken Johnson
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