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

[Adam Tarr]

At 08:55 AM 2/26/2004 -0800, Ernest Prabhakar wrote:

>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.

Good work Ernie.  As I said in an earlier response, "[Ken Johnson's] 
mention of "large voting populations" is crucial, since it allows me to 
assume that the marginal utility for an additional ranking point given to 
candidate B remains constant through the entire 0->100 range. On a small 
committee, this may not be the case, so it's possible (I'm not sure) that 
intermediate rankings make sense in that case."

So this would be just such a case, where due to the extremely precise 
knowledge and the hair's-breadth nature of the election, the marginal 
utility for each additional point for candidate C is not constant.  If we 
were to make this election have a plausible level of uncertainty, say:

>(I) 40% chance:
>A: 101,000
>B: 102,000
>C: 104,000
>
>(II) 60% chance:
>A: 100,000
>B: 104,000
>C: 105,000

Then the optimal strategy is to give B 5 points if the preference gap 
between C and B is at least twice as big as the preference gap between A 
and B, and one point if it is not.

-Adam