# [EM] New voting system website. Comments sought.

Markus Schulze schulze at sol.physik.tu-berlin.de
Fri Aug 18 05:39:48 PDT 2000

Dear Mike,

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.

Markus Schulze
schulze at sol.physik.tu-berlin.de
schulze at math.tu-berlin.de
markusschulze at planet-interkom.de