CR == Approval? Re: [EM] Re: Election-methods digest, Vol 1 #517 - 3 msgs

[Ernest Prabhakar]

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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