Schulze Method

<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"> <HTML> <HEAD> <TITLE> Schulze Method </TITLE> <LINK REL="Index" HREF="index.html" > <LINK REL="made" HREF="mailto:election-methods%40lists.electorama.com?Subject=Re%3A%20Schulze%20Method&In-Reply-To=%3C3.0.1.32.19981114164904.0097dda0%40sol.physik.tu-berlin.de%3E"> <META NAME="robots" CONTENT="index,nofollow"> <style type="text/css"> pre { white-space: pre-wrap; /* css-2.1, curent FF, Opera, Safari */ } </style> <META http-equiv="Content-Type" content="text/html; charset=us-ascii"> <LINK REL="Previous" HREF="068095.html"> <LINK REL="Next" HREF="068102.html"> </HEAD> <BODY BGCOLOR="#ffffff"> <H1>Schulze Method</H1>  <B>Markus Schulze</B> <A HREF="mailto:election-methods%40lists.electorama.com?Subject=Re%3A%20Schulze%20Method&In-Reply-To=%3C3.0.1.32.19981114164904.0097dda0%40sol.physik.tu-berlin.de%3E" TITLE="Schulze Method">schulze at sol.physik.tu-berlin.de </A><BR> <I>Sat Nov 14 07:49:04 PST 1998</I> <P><UL> <LI>Previous message: <A HREF="068095.html">U.K. Government Defeated Again, etc. (FWD) </A></li> <LI>Next message: <A HREF="068102.html">[EM] Suggested Election Plan for any State </A></li> <LI> <B>Messages sorted by:</B> <a href="date.html#68099">[ date ]</a> <a href="thread.html#68099">[ thread ]</a> <a href="subject.html#68099">[ subject ]</a> <a href="author.html#68099">[ author ]</a> </LI> </UL> <HR>   <PRE>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 </PRE>   <HR> <P><UL>  <LI>Previous message: <A HREF="068095.html">U.K. Government Defeated Again, etc. (FWD) </A></li> <LI>Next message: <A HREF="068102.html">[EM] Suggested Election Plan for any State </A></li> <LI> <B>Messages sorted by:</B> <a href="date.html#68099">[ date ]</a> <a href="thread.html#68099">[ thread ]</a> <a href="subject.html#68099">[ subject ]</a> <a href="author.html#68099">[ author ]</a> </LI> </UL> <hr> <a href="http://lists.electorama.com/listinfo.cgi/election-methods-electorama.com">More information about the Election-Methods mailing list</a><br>  </body></html>

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Schulze Method