[EM] Re: Sprucing up vs. Condorcet Lottery vs. immunity: The "twisted prism" example

[Ted Stern]

On 20 Jan 2005 at 14:54 PST, Ted Stern wrote:
> So your defeat rankings should actually be
>         Bi>Ai       , strength 11 (the 3 "straight upward" beats)
>         A1>A2>A3>A1 , strength 10 (the "upper clockwise" 3-cycle)
>         B1<B2<B3<B1 , strength 10 (the "lower counter-clockwise" 3-cycle)
>         Ai>Bj (i!=j), strength 8  (the 6 "diagonal downward" beats)

Hi Jobst,

One other comment about the twisted prism example:  If defeats are sorted
using approval-weighted pairwise, you get an approval weighted defeat matrix
like this:

        -  4  0  0  4  8
        0  -  4  8  0  4
        4  0  -  4  8  0
        3  0  0  -  0  4
        0  3  0  4  -  0
        0  0  3  0  4  -
      
      Ai>Bj (i!=j), strength 8
      A1>A2>A3>A1 , strength 4
      B1<B2<B3<B1 , strength 4
      Bi>Ai       , strength 3

With this ranking, immune methods will drop the Bi>Ai defeats, and you won't
get the paradox you found originally.

In my opinion this is a(nother) strong argument in favor of combining
RP/Beatpath/River with approval weighting.

Ted
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