[EM] proposal: weighted pairwise comparison

[Brian Olson]

On Jun 10, 2004, at 3:11 PM, Dgamble997 at aol.com wrote:

>  45 A 100 > B 70 > C 0
>  10 B 100 > A 70 > C 0
>  5  B 100 > C 70> A 0
>  40 C 100 > B 70 > A 0
>
>
>  45 A 100 > B 10 > C 0
>  10 B 100 > A 90 > C 0
>  5  B 100 > C 90 > A 0
>  40 C 100 > B 10 > A 0
>
>  >Yup. Both are decided by plain Condorcet, which only considers 
> rankings
>  >not ratings, and B wins. Of the methods on my Election Calculator, 
> only
>  >IRV selects A. B is the compromise candidate. Everyone is happy 
> enough
>  >with B
>
>  >In your second example, B being devalued and B-voters throwing in 
> more
>  >with A, IRNR picks this up and selects A (rank-only methods other 
> than IRV
>  >still choose B):
>
>  Thanks for putting my examples into your Election Calculator. One 
> question though, how does it translate the cardinal ratings into 
> Approval ballots?
>
>  Your Election Calculator translates both examples into the Approval 
> result:
>
>  A 55
>  B 100
>  C 45
>
>  Surely using the zero information strategy of  "approve all 
> candidates whose cardinal rating  is greater than the mean cardinal 
> rating" the second example should give the Approval result:
>
>  A 55
>  B 15
>  C 45

Hmm, Perhaps I ought to implement that zero-info strategy. What it 
actually does right now is that any rating greater than zero counts as 
approval. I normally think of ratings in positive-negative scales, -1.0 
to 1.0, -100 to 100, etc. Of course that voting strategy is applicable 
no matter what the range. It might make it easier to compare Approval 
against other methods, instead of having to shuffle ratings around zero 
to use the fixed approval cutoff.

Brian Olson
http://bolson.org/