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Re: Nov 16 draft of voting mechanics

On Sun, Nov 17, 2002 at 12:12:53AM +0100, Jochen Voss wrote:
> trying to actually implement the algorithm from the draft turns out to
> be a good test :-)

Ok.  Note that I've not sat down and read your implementation, yet.

> 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    -

Just as a note: in my view of the world, where you put a "-",
I'd put a "0".  In principle this shouldn't matter, but maybe
that has something to do with what you consider ambiguous?

> 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).

I ran through the steps by hand, and I agree.  [You didn't say,
but the rows in your matrix have to represent the vote count "for"
an option, and the columns the vote count "against", otherwise
the default option would defeat everything else.]

Out of curiosity, how did you generate that set of tallies?  Did you start
from some set of ballots, or did you just randomly generate some numbers?

> 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?

I had meant to change ii. so that it read something like:

"Unless this would eliminate all vote counts in the propositions of the
Schwartz set, the vote counts of the weakest propositions are eliminated."

Is that better?



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