[EM] Re: Sprucing up MMPO and other methods

[Ted Stern]

On 28 Dec 2004 at 13:40 PST, Ted Stern wrote:
> I think it is possible to show that every 4-candidate cycle can be reduced
> to 3 candidates this way.  Can you verify this?  This would take care of all
> RP/BP/River differences in the 4 candidate case.  Five candidates might be
> tougher, but you get the general idea, right?  You could determine which
> sets of 10 cyclic defeats are short-beatpath irreducible or reduce to 4
> candidates, and then examine only the ranked permutations of those sets.
> Sounds like a job for Jobst ...

With a little thought, I realized that with the following cyclic M matrix for
5 candidates, every candidate is uncovered, since each candidate has at
beatpaths of length 1 or 2 to every other one:  

          {AB,AC,BC,BD,CD,CE,DE,DA,EA,EB}

M =

  0  1  1  0  0
  0  0  1  1  0
  0  0  0  1  1
  1  0  0  0  1
  1  1  0  0  0

M^2 =

  0  0  1  2  1
  1  0  0  1  2
  2  1  0  0  1
  1  2  1  0  0
  0  1  2  1  0

M + M^2 =

  0  1  2  2  1
  1  0  1  2  2
  2  1  0  1  2
  2  2  1  0  1
  1  2  2  1  0

Ted
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Frango ut patefaciam -- I break that I may reveal