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Schulze Method

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  • Markus Schulze
    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
    Message 1 of 2 , Nov 14, 1998
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      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
    • Blake Cretney
      ... Did Schwartz specify margins, VA, or did he not consider cases without full rankings. ... Blake ... http://www.dejanews.com/ Easy access to 50,000+
      Message 2 of 2 , Nov 15, 1998
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        On Sat, 14 Nov 1998 16:49:04 Markus Schulze wrote:
        >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.

        Did Schwartz specify margins, VA, or did he not consider
        cases without full rankings.

        ---

        Blake


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