[Election-Methods] [EM] Intermediate Ratings Never Optimal?

[Abd ul-Rahman Lomax]

At 04:19 PM 7/23/2007, Stephane Rouillon wrote:
>It means that a non-extreme range votes ballot can be optimal, but if it is
>the case,
>at least two extreme range votes ballot should be optimal too.

I may be thoroughly confused here, but there are some unclear 
definitions. It is trivial that an optimal Range ballot contains the 
extremes. The question is whether or not the voter's individual 
utility can be improved, in an election with more than two 
candidates, by usingca an intermediate rating (or perhaps more than 
one, if there are three or more candidates).

What has been claimed is that it is *never* optimal to cast 
intermediate votes. What is clearly true about this is that it is 
never optimal to submit a ballot that does not contain at least one 
instance of both extremes. And that's also a trivial result. 
Submitting a ballot with, for example, votes of 0, 0, 0.5 (1 being 
full-scale), is essentially casting one-half vote, devaluing the 
personal utilities of the voter.

But this does not necessarily apply to candidates other than the most 
preferred or least preferred. Casting an extreme vote in the positive 
direction, for such a third candidate, improves the possibility of 
election of that candidate over the least preferred, but 
simultaneously abstains from the pairwise election between the 
favorite and the least-preferred.

I somewhat thought that I would find equivalence in the case studied, 
since the B preference was midrange. That's not what I found, so I 
may have erred, it's certainly worth looking again!

I had thought I would have to go to Range 3 (0-3), with sincere 
utilities of 3, 2, 0, to find the effect I expected, because here an 
approval style vote clearly distorts, and I was just trying the Range 
2 case to practice and to see what a simpler case looked like.