[EM] Droop fails the Markus Schulze Rule

[Craig Carey]

At 13:07 16.10.99 , Donald E Davison wrote:
>Greetings,
>
>Markus Schulze wrote:
>     "I think, that the aim of proportional representation is to minimize
>the number of the wasted votes."
>
>Donald:  I liked this statement so much that I decided to make it a rule -
>I call it The Markus Schulze Rule.
  Schulze Rule Opus 1.
>

The word "aim" has been used.
The words "wasted vote" may be difficult to define. An outstanding
 method could be both simple but able to be understood. They need
 not be like STV. So votes could be altered a little and if the
 outcome changes then they are not wasted. However ratios of papers
 could have the point corresponding to the papers far distant
 from all m boundaries, where m is the number of winners.

The Rule Mr Davidson just defined or named, contains the undefined
 idea "wasted votes".
----------------------------------------------------------------

Whether a vote is wasted or not can be unclear.

Proportionality could be worded as follows...

(1) Election system V, V =
  a  A
  b  BCDA
  c  C
  d  DCAB

(2) Constraints (P1) or etc, and whatever else

(3) The boundaries could start out being those of multiwinner FPTP,
   E.g. Winners = Max(m; (a,b,c,d)) where the function returns
    the m largest (most positive) numbers in the list.

(4) The ideal boundaries could be said to be
        Winners = Max(m; S), S = (a+b+d, b+d, b+c+d, b+d)

        Let the list in the 2nd be called S, S

    While those boundaries are clearly not desirable, they are
     never going to be obtained unless the constraints are defined
     in a way that allows that.

(5) This constraint could be added, an why not?:

   For all c (c is a candidate) [

      (c in Max(m; a,b,c,d)) => (c in W) => (c in Max(m; S)) ]

   That says that if a candidate wins or loses both (3) & (4),
    then it has the same win-lose state in final outcome.

(6) The idea gets a bit vague: the boundaries could be optimised
   away from (3), and towards (4).
   A single method could be so derived. A numerical derivation
   is one possibility.

Then after a year and a sabbatical, the results could be put aside.
 and a new paper published. Clearly not by Riker.

>Regards,
>Donald




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Mr G. A. Craig Carey                   E-mail: research at ijs.co.nz
Auckland, Nth Island, New Zealand
Pages: Snooz Metasearch: http://www.ijs.co.nz/info/snooz.htm
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