[EM] Efforts to improve on CR's strategy

[Ken Johnson]

>Message: 1
>Date: Fri, 21 May 2004 22:06:52 +0200 (CEST)
>From: =?iso-8859-1?q?Kevin=20Venzke?= <stepjak at yahoo.fr>
>...
>This is not realistic unless you think voters are all extremists and only the
>candidates show moderation.
>...
>Kevin Venzke
>  
>
Kevin,

It's not so much a matter of them being extremists as being simpletons. 
All the liberal voters approve all of the liberal candidates, and all of 
the conservative voters approve all of the conservative candidates. So 
all the liberal candidates are tied and so are the conservative 
candidates. None of the other election methods exhibits this behavior.

Which brings me back to the original topic: Can CR be improved? I hope 
someone will pick up on this topic because I would be very interested in 
people's opinions about this. The proposed "Normalized CR" method is as 
follows:
(1) Voters give candidates CR ratings. There no need for any range limit 
- any finite CR value, positive or negative, can be allowed.
(2) Apply an additive shift to each voter's CR profile so that the sum 
of the absolute values is minimized.
(3) Apply a multiplicative scale factor to each voter's CR profile so 
that the sum of the absolute values is 1.
(4) After applying the above transformations, select the candidate with 
the highest average CR.

The basic idea is that scaling the sum of the absolute values to 1 is a 
better way of limiting individual voting power than restricting 
individual CR's to a fixed range (e.g. 0 to 1). With a fixed range, the 
optimum strategy is to give all candidates polarized ratings - 
equivalent to Approval. But the above normalization process removes the 
incentive for voters to polarize their ratings, and they are more likely 
to vote sincerely. (At least that's my hypothesis, I'm not sure if it's 
actually true.)

The additive shift is applied because it is strategically advantageous 
to the voter. (If the scale factor were not applied the additive shift 
would have no effect on the election. With the scale factor, the 
additive shift maximizes voting power by making the scale factor as 
large as possible.)

Does anyone have thoughts on how this form of Normalized CR would 
perform and how it compares to other methods?

Ken Johnson