On Feb 26, 2004, at 5:46 AM, Adam Tarr wrote:
Ernest Prabhakar wrote:However, it seems like there can well be extreme cases, due to either detailed information or sub-optimal strategic behavior by opponents, where a different strategy would actually be more -effective- (optimal doesn't mean perfect). Thus, in those cases, the most effective strategy for CR would not be precisely identical to Approval, simply because the scenarios are slightly different.
"It seems like" is not very convincing. Providing an example of such a case would be more convincing.
I was more suggesting than trying to convince, but I suppose I can provide an example. Suppose the election is CR with three candidates (A, B,C) who must be ranked from 1 to 5. Let us say that based on the information that Voter X has, the likely ranking by other voters will end up being either:
(I) 40% chance: A: 101 B: 102 C: 104
(II) 60% chance: A: 100 B: 104 C: 105
Now, if Voter X's true preference is A > B > C, the most effective ranking in this particular case is:
A: 5 B: 3 C: 1
In case (I), this means his preferred A can win, whereas in case (II) it at least his second-choice B will beat the despised C.
Of course this is a highly unusual level of information, and probably can only happen if the other voters are acting non-strategically,. However, the very fact such a counterexample exists means that the most effective CR voting strategy not always precisely identical to Approval under all circumstances, which is why I think it is better to use less confusing terminology.
-- Ernie P.
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