Hello Raul, trying to actually implement the algorithm from the draft turns out to be a good test :-)
On Sat, Nov 16, 2002 at 12:48:07PM -0500, Raul Miller wrote:
> ii. Unless this would eliminate all options in the Schwartz set,
> the weakest propositions are eliminated.
> [...]
>
> Definition: A proposition is eliminated by treating both
> of its vote counts as zero from this point forward.
>
> iii. If eliminating the weakest propositions would eliminate all
> votes represented in the Schwartz set, a tie exists [...]
What does "eliminate all options" and "eliminate all votes" mean
in this context? Could we formalise this?
Example: (X is the default option)
A B C D X
A - 24 17 25 31
B 25 - 26 24 29
C 31 24 - 31 30
D 25 26 18 - 27
X 15 18 15 18 -
If my algorithm is correct, than just before step 6.ii the
Schwartz set consists of options B, C, and D and the
weakest propositions are (B,C) and (B,D).
This leads to the following new matrix:
B C D
B - 0 0
C 0 - 31
D 0 18 -
I guess that C is the winner here. But what condition should my
program check to see whether "this would eliminate all options in the
Schwartz set"? Maybe whether all entries in the matrix become zero?
Jochen
--
Omm
(0)-(0)
http://www.mathematik.uni-kl.de/~wwwstoch/voss/privat.html
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