Schulze Method

Markus Schulze schulze at sol.physik.tu-berlin.de
Sat Nov 14 07:49:04 PST 1998

```Dear participants,

because of recent criticism by Blake Cretney ("Schulze
tie-breaker, monotonicity problems," 03 Nov 1998), the
aim of this e-mail is to reformulate the Schulze method.

******

Step 1:

Calculate the Schwartz Set of the remaining candidates and
eliminate all those candidates, who are not in the Schwartz
Set of the remaining candidates.

If there is only one candidate remaining, then go to Step 4.
Otherwise go to Step 2.

******

Step 2:

If there are still pairwise inequalities between remaining
candidates, then substitute the "weakest" pairwise inequality
between two remaing candidates with a pairwise equality and
go to Step 1. Otherwise go to Step 3.

[The "weakest" pairwise inequality is that pairwise inequality
with the smallest absolute number of votes for the winner of
this pairwise inequality. If there is more than one pairwise
inequality with the smallest absolute number of votes for the
winner of this pairwise inequality, then the "weakest" pairwise
inequality is that pairwise inequality (among those pairwise
inequalities with the smallest absolute number of votes for the
winner) with the largest absolute number of votes for the loser.
If there is more than one pairwise inequality with the smallest
absolute number of votes for the winner and the largest absolute
number of votes for the loser, then all these inequalities are
substituted with a pairwise equality simultaneously.]

******

Step 3:

If there is a ballot, that hasn't yet been chosen randomly,
then -among those ballots that haven't yet been chosen randomly-
choose one ballot randomly. Restart the whole algorithm among
those remaing candidates, that are (among the remaining
candidates) top-ranked on this randomly chosen ballot and
eliminate the other remaining candidates. [Already eliminated
candidates stay eliminated even after the restart of the
algorithm.]

Otherwise, choose the winner randomly among the remaing
candidates and go tho Step 4.

******

Step 4:

The remaing candidate wins the election.

Markus Schulze

```