[EM] New voting system website. Comments sought.

MIKE OSSIPOFF nkklrp at hotmail.com
Sat Aug 19 08:24:00 PDT 2000

```

>Russ Paielli writes:
> > Schwartz Sequential Dropping (SSD)
> >
> > The Schwartz Sequential Dropping (SSD) method works
> > as follows: drop the weakest defeat among an innermost
> > unbeaten set, repeating if necessary until one of the
> > candidates is unbeaten. An unbeaten set is a set of
> > which none are beaten by anyone outside the set. An
> > innermost unbeaten set is an unbeaten set that doesn't
> > contain a smaller unbeaten set. In the absence of ties
> > and defeats of equal magnitude, there can be only one
> > innermost unbeaten set. The ordered list of defeats for
> > the example is repeated here for convenience:
> >
> >    1.D/B:60
> >    2.B/C:50
> >    3.A/B:40
> >    4.C/A:30
> >    5.C/D:25
> >    6.D/A:20
> >
> > The SSD method proceeds as follows for the example:
> > Initially there's no unbeaten set except for the entire set
> > of candidates, so the entire set is an innermost unbeaten
> > set. Every defeat therefore involves the innermost unbeaten
> > set. The weakest of those defeats is D/A, so it is dropped.
> > Now {A,B,C} is an innermost unbeaten set. The weakest defeat
> > among {A,B,C} is C/A, so it is dropped. Candidate A is now
> > unbeaten. So A wins.
>
>Either Russ Paielli's example is incorrect or your claim
>that SSD is identical to Schulze at least when there are no
>pairwise ties is incorrect.

Yes, I miscounted the example. After dropping DA, I didn't
notice DB, and so I thought that D was no longer in the innermost
unbeaten set. Because of DB, it still is, and so the unbeaten set
is still the set of all the candidates. So the next defeat dropped
is CD25. So D wins in SSD, as it does in Schulze.

I'll tell Russ about the error, and correct the SSD example count.

Thanks for pointing that out.

Mike Ossipoff

________________________________________________________________________
Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com

```