- 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 - On Sat, 14 Nov 1998 16:49:04 Markus Schulze wrote:
>Dear participants,

Did Schwartz specify margins, VA, or did he not consider

>

>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.

cases without full rankings.

---

Blake

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