Talk:Schulze method/Archive 2

Implementation Question
The article doesn't seem to be in line with the original paper.

The article says to start the path search with: 1 for i : = 1 to C 2 begin 3   for j : = 1 to C 4   begin 5      if ( i ≠ j ) then 6      begin 7         if ( d[i,j] > d[j,i] ) then 8         begin 9            p[i,j] : = d[i,j] 10         end 11         else 12         begin 13            p[i,j] : = 0 14         end 15      end 16   end 17 end

However, the paper says to start the path search with: 1 for i : = 1 to C 2 begin 3   for j : = 1 to C 4   begin 5      if ( i ≠ j ) then 6      begin 9            p[i,j] : = d[i,j] - d[j,i] 15      end 16   end 17 end

See Article 1, page 8 and Article 2, page 3.

Also, some of the provided articles have yet another way of writing this step, which adds to my confusion. See Article 3, page 24.

Are the two different ways equivalent? Which one is correct? And, does Article 3 have a typo in it? —Preceding unsigned comment added by 208.124.58.110 (talk) 21:19, 15 October 2007 (UTC)


 * Paper1 is only a short summary of paper2. As paper1 should be as short as possible, it discusses only margins as a measure for the strength of a pairwise defeat (This means: The pairwise defeat CD is stronger than the pairwise defeat EF if and only if d[C,D] - d[D,C] > d[E,F] - d[F,E].) because for this measure the proofs are very short and simple.


 * However, as winning votes is the most frequently used measure for the strength of a pairwise defeat in those organizations that are using the Schulze method and as Wikipedia articles don't contain mathematical proofs, the Wikipedia article uses winning votes. Winning votes means that the pairwise defeat CD is stronger than the pairwise defeat EF if and only if at least one of the following conditions is satisfied:


 * d[C,D] &gt; d[D,C] and d[E,F] &le; d[F,E].
 * d[C,D] &ge; d[D,C] and d[E,F] &lt; d[F,E].
 * d[C,D] &gt; d[D,C] and d[E,F] &gt; d[F,E] and d[C,D] &gt; d[E,F].


 * Paper2 discusses the Schulze method in a more general manner and treats the definition for the strength of a pairwise defeat as a parameter. Markus Schulze 11:22, 16 October 2007 (UTC)

Three questions
Hello, I want to translate this article in french and I have three questions

About path heuristic
This condition
 * For i = 1,...,(n-1): d[C(i),C(i+1)] &gt; d[C(i+1),C(i)].

seems very strong. What happens if d[C,Y] ≤ d[Y,C] for every candidate C. Is there no path from X to Y ?


 * The definition says:


 * A path from candidate X to candidate Y of strength z is an ordered set of candidates C(1),...,C(n) with the following four properties:


 * C(1) is identical to X.
 * C(n) is identical to Y.
 * For i = 1,...,(n-1): d[C(i),C(i+1)] &gt; d[C(i+1),C(i)].
 * For i = 1,...,(n-1): d[C(i),C(i+1)] &ge; z.


 * If there is a p such that there is a path from candidate A to candidate B of strength p and no path from candidate B to candidate A of strength p, then candidate A disqualifies candidate B.


 * Therefore, if there is a path from candidate A to candidate B and no path from candidate B to candidate A, then candidate A disqualifies candidate B. Markus Schulze 14:47, 23 June 2006 (UTC)

What about p[X,Y] ?


 * If there is no path from candidate A to candidate B, then p[A,B] : = 0. Markus Schulze 15:56, 23 June 2006 (UTC)

About Schwartz heuristic
I don't know how to respect the rules in this example (10 voters; 5 candidates):


 * 3 ABCED
 * 4 DECBA
 * 1 BADCE
 * 1 CBAED
 * 1 EADCB

Here, the Schwartz set is ABCDE (yes ?), there are some defeats (yes ?), and I dont know what is the weakest defeat


 * Yes, the Schwartz set is ABCDE. The weakest defeats are A:D, B:A, C:B, and D:C each with a strength of 6:4 votes. If the weakest defeat is not unique, then all defeats that are tied for weakest defeat are dropped simultaneously. Therefore, the defeats A:D, B:A, C:B, and D:C are dropped simultaneously. Now, all candidates are tied with each other; thus, all candidates are tied for winner. Markus Schulze 15:56, 23 June 2006 (UTC)

Or, easier, what is the weakest defeat in the example 1 (path heuristic)? Wich candidate must be eliminated ?


 * In example 1 (path heuristic), the weakest defeat is E:A = 23:22. Markus Schulze 15:56, 23 June 2006 (UTC)

Name
The two heuristics are very different. Why are they both called "Schulze method" ?

Thanks (please I'm french, write your answer in simple english). HB, 22 Jun 2006


 * Both heuristics, the path heuristic and the Schwartz heuristic, have been proposed by Markus Schulze. Both heuristics describe the same method, in so far as they always find the same winner. As the properties of the Schulze method don't depend on the heuristic used, it makes sense simply to use the term "Schulze method" to refer to both heuristics. Markus Schulze 14:47, 23 June 2006 (UTC)


 * You wrote:


 * Ils sont fous ces wikipediens!!! Déjà que Condorcet lui-même trouvait sa méthode compliquée. Avec Schulze méthode du chemin, c'est la prise de tête garantie. Je ne suis pas sûre que ceux qui ont voté pour Condorcet Schulze aient bien lu l'article en anglais, sinon ils auraient au moins posé la question "Schulze méthode du chemin (argh....) ou Schulze méthode Schwartz?"


 * Both heuristics for the Schulze method always choose the same winner. Therefore, when an organization discusses whether the Schulze method should be adopted, there is no need to discuss which of these heuristics should be adopted. It is sufficient to say that the Schulze method should be adopted. Markus Schulze 06:33, 24 June 2006 (UTC)

Thanks for your very clear answers. HB, 24 Jun 2006

Heuristic + restructuralization of the article
I thing this is a very bad word leading to confusion (I will use the word algorithm instead, but may be there is something better). For the article to be written clearly I would suggest the following schema:

First paragraphs with general definition od SSD (roughly as it is now).

Than the paragraph which briefly sumarizes the ideas used to solve the circular ambiguities (I mean ideas common to all heuristics). I leave to discussion if more exact definition of the method should be included here (other than the equivalence to either of algorithms).

Than some sentence like: There are more algorithms which reach always identical results, therefore all of them can be refered as Schulze method. The algorithms are following:

Than subchapters describing all (both) algorithms in detail.

What do you think?

--Gorn 03:41, 24 September 2006 (UTC)

Examples
In the Path Heuristic, there is a number in front of the ordering of the votes. "3 ABCED". Maybe I'm missing something, but the text doesn't seem to explain what those number are and what they mean, or at least it doesn't do so near the first example. I'd like to see that improved because it's interfering with my understanding of the explanation of the examples. Hu 07:04, 30 October 2006 (UTC)


 * The numbers mean how many voters have chosen that order of the candidates. -- Jokes Free4Me (talk) 21:55, 30 December 2007 (UTC)

4th example
I see that in the 4th example, both B and D are potential winners. What happens next? -- Jokes Free4Me (talk) 21:55, 30 December 2007 (UTC)


 * There are many ways to solve situations with more than one potential winner. For example, Debian's constitution says in appendix A ("Standard Resolution Procedure"), article A6 ("Vote Counting"), section 8: "If there are multiple options, the elector with the casting vote chooses which of those options wins."


 * In section 5 of my paper, I recommend that, when there is more than one potential Schulze winner, then the ranked pairs method should be used to calculate a complete ranking of all candidates (and not only of the potential Schulze winners) and the final winner should be that potential Schulze winner who is ranked highest in this ranked pairs ranking. However, in example 4, also the ranked pairs method is indecisive between the rankings BCDA, BDAC, and DABC. Markus Schulze 15:38, 2 January 2008 (UTC)


 * I guess B could still argue for a win because he would beat D in a run-off, and he also has a better wins/defeats matchup (2-1 while D has 1-2). Are there any arguments for D winning? :-) -- Jokes Free4Me (talk) 17:20, 4 January 2008 (UTC)


 * (1) You wrote: "B would beat D in a run-off." Simply re-applying the Schulze method among the potential winners could result in a violation of monotonicity.


 * (2) You wrote: "B has a better wins/defeats matchup." B and C are clones. When we shrink them to a single candidate B, example 4 looks as follows:


 * 3 ABD
 * 2 DAB
 * 2 DBA
 * 2 BDA


 * {| border=2

! !!bgcolor=#ddffdd| d[*,A] !!bgcolor=#ddffdd| d[*,B] !!bgcolor=#ddffdd| d[*,D] !bgcolor=#ddffdd| d[A,*] !bgcolor=#ddffdd| d[B,*] !bgcolor=#ddffdd| d[D,*]
 * || 5 || 3
 * 4 ||  || 5
 * 6 || 4 ||
 * +The matrix of pairwise defeats looks as follows:
 * }
 * }


 * Now, all candidates have the same wins/defeats matchup.


 * (3) You wrote: "Are there any arguments for D winning?" Yes! Reversal symmetry! Original situation:


 * There are three candidates. Candidate B pairwise beats candidate D. Candidate D pairwise beats candidate A. Candidate A pairwise beats candidate B. The pairwise defeats B:D and A:B have the same strength. The pairwise defeat D:A is stronger.


 * When the individual ballots are inverted, then we get:


 * There are three candidates. Candidate D pairwise beats candidate B. Candidate A pairwise beats candidate D. Candidate B pairwise beats candidate A. The pairwise defeats D:B and B:A have the same strength. The pairwise defeat A:D is stronger.


 * The original situation and the inverted situation are identical; only the roles of candidate D and candidate A have been exchanged. So if candidate B was the unique winner in the original situation, then he must also be the unique winner in the inverted situation. But this would be a violation of reversal symmetry.


 * I recommend that, in situations where both the Schulze method and the ranked pairs method are indecisive, random ballot should be used to decide who of the potential winners should be elected. That means: A ballot is chosen randomly; the winner is that potential winner who is ranked highest on this randomly chosen ballot. In example 4, B would be elected with a probability of 5/9 and D would be elected with a probability of 4/9. Markus Schulze 11:36, 6 January 2008 (UTC)

Non-strict ordering
If it is not too much trouble, i'd like to see one example that features non-strict orderings of the candidates, something like: Thank you. -- Jokes Free4Me (talk) 21:55, 30 December 2007 (UTC)
 * A, then D, then C, with B and E not ranked
 * B and C ranked the same for 1st position, then D, then A, then E


 * Section 3.6 of my paper contains an example with non-strict orderings. Markus Schulze 17:29, 5 January 2008 (UTC)

Criteria
The criteria section of the article is complex. I was wondering if someone had a good idea on how to group the criteria. For example, half of the criteria on the list are implied by local IIA: non-imposition, non-dictatorship, majority, mutual majority, Condorcet and Condorcet loser, Smith, and LIIA itself.

I thought that an implication list would work but the limitation of the format in not allowing multiple inheritance was unfortunate. Perhaps a sub-list?
 * 1) Schwartz criterion → Smith criterion → mutual majority criterion → majority criterion → non-imposition
 * 1) Schwartz criterion
 * 2) Smith criterion
 * 3) Mutual majority criterion
 * 4) Condorcet criterion
 * 5) Condorcet loser
 * 6) Majority criterion
 * 7) Non-dictatorship
 * 8) Non-imposition
 * 9) Independence of clones

Of course perhaps this is a bad idea and the criteria should stay as-is, on which case the criteria not met should probably follow suit for consistency.

CRGreathouse (t | c) 04:48, 6 November 2007 (UTC)


 * The implications of the different criteria can be quite complex (e.g. see section 2.1 of my paper). Therefore, it makes more sense, in my opinion, to describe these implications in the corresponding voting system criterion articles rather than in the voting system articles.


 * By the way: Why did you delete the duplicate links? I believe that most readers do not read Wikipedia articles from top to bottom. They only read those parts they consider interesting. Therefore, it makes more sense, in my opinion, to wikify all occurrences of a given term in a given article rather than to wikify only the first occurrence of this term in this article. Is there a Wikipedia policy about duplicate links? Markus Schulze 20:35, 6 November 2007 (UTC)


 * The duplicate links I deleted were to aka, three links in 3-5 lines. I don't think that was needed even once, but three times was certainly over the top IMO.  Wikipedia policy on duplicate links: link first occurrence in the article, and possibly the first occurrence in each section (editor discretion), but not more than one link to a given page per section.  I apply this loosely; whatever serves the particular article works well enough for me.  But I certainly don't like multiple links to the same thing in a section.  I don't mind the ones like non-imposition and non-dictatorship both going to the same place -- that's where the ignore all rules policy comes in. :)
 * I have a chart similar to yours (with the eight majoritarian properties you have, plus five unanimity properties) on my website. I don't think the relations are all that complex.  Maybe we could just combine those that follow from the Condorcet property?  On this list that would be the mutual majority criterion, majority criterion, non-dictatorship, non-imposition, and the Condorcet criterion itself.
 * CRGreathouse (t | c) 21:12, 6 November 2007 (UTC)


 * Where is your website? Markus Schulze 22:22, 6 November 2007 (UTC)


 * I cringe to show it, as most of the pages are in progress. Here's the page with the chart: . CRGreathouse (t | c) 21:52, 9 November 2007 (UTC)


 * If there are less than 3 voters, then near-unanimity doesn't make any sense. If there are 3 or more voters, then majority criterion implies near-unanimity. Markus Schulze 21:58, 9 November 2007 (UTC)


 * Yes, and Smith doesn't imply Condorcet loser unless there are at least 2 candidates. I have some decisions to make still, and I want to add more criteria.  My problem at the moment is reconciling different systems -- I like the Pattanaik & Peleg random model, for example, but most of the criteria would need to be re-written to include such a model.  Many of the criteria should be expanded in some way, or don't quite work in a general framework.  For example strong Pareto is implied by a suitably generalized Schwartz criterion, but my version was taken from a paper using a single-winner version.  Should I generalize?  If so, how do I name the criteria?  Smith's criterion (he calls it the "Condorcet criterion", though he notes that it's an extended version of same) is actually a multiple-winner version working on all unbeaten subsets of the set of candidates, not just the "Smith set" -- how should I expand to cover that?  Again, lots of decisions to make. CRGreathouse (t | c) 22:12, 9 November 2007 (UTC)

I realize monotonicity is generally passed by almost all methods, but should it be added to the table? - McCart42 (talk) 23:47, 17 December 2007 (UTC)


 * Monotonicity is already added. Markus Schulze 23:53, 17 December 2007 (UTC)

Bringing BetterPoll to Facebook
If anyone wants to help with a Schulze method implementation on Facebook, feel free to contact Dave Scotese: http://www.facebook.com/profile.php?id=772980030 - McCart42 (talk) 23:54, 17 December 2007 (UTC)

Difference from Ranked Pairs
I'm new to the topic, and a bit confused about the difference between Ranked Pairs and the Schulze method... Would someone please provide (or link to) an example where they result in a different winner given the same votes? --Explodicle (talk) 21:00, 20 March 2008 (UTC)


 * In example 1 of the Schulze method article, the Schulze method chooses E while Ranked Pairs chooses A. In example 2, the Schulze method chooses D while Ranked Pairs chooses A. In example 3, the Schulze method chooses B while Ranked Pairs chooses A. Markus Schulze 22:00, 20 March 2008 (UTC)


 * Sections 3.1 and 9 of this paper might be interesting. Markus Schulze 21:36, 20 March 2008 (UTC)


 * The main difference between the Schulze method and Ranked Pairs is that the winner of the Schulze method is almost always identical to the winner of the MinMax method, while the winner of the Ranked Pairs method differs from the winner of the MinMax method needlessly frequently. Examples:


 * Norman Petry (who uses the term "Tideman" for Ranked Pairs and the term "plain Condorcet" for the MinMax method) made some simulations and observed that the number of situations, where the Schulze method and the MinMax method chose the same candidate and Ranked Pairs chose a different candidate, exceeded the number of situations, where Ranked Pairs and the MinMax method chose the same candidate and the Schulze method chose a different candidate, by a factor of 100.
 * Jobst Heitzig (who uses the term "beatpath" for the Schulze method, the term "Tideman" for Ranked Pairs, and the term "plain Condorcet" for the MinMax method) made a thorough investigation of the 4-candidate case. In no situation, the Schulze method and the MinMax method chose different candidates. ("Beatpath and Plain Condorcet are unanimous in all these examples!") But in 96 situations, Ranked Pairs and the MinMax method chose different candidates.


 * In section 4.8 of this paper, I explain why the winner of the Schulze method is almost always identical to the winner of the MinMax method. Markus Schulze 11:32, 21 March 2008 (UTC)


 * Ok, now I see. Thanks! --Explodicle (talk) 18:02, 27 March 2008 (UTC)

Re: Comparison with other preferential single-winner election methods
I notice that there are no "No"s listed for the Schulze method. Are there really no criteria/properties that this method fails and others don't? If so, this should be stated explicitly and referenced, because otherwise the table looks suspect. 82.139.87.64 (talk) 04:13, 19 June 2008 (UTC)


 * All methods capable of choosing from among three or more alternatives fails some criterion. In regards to Schulze one criterion of interest is independence of strongly dominated alternatives a/k/a independence of pareto dominated alternatives.  Both Schulze and ranked pairs fail it, but Heitzig's river method (which is often compared to Schulze and ranked pairs) passes. SgtSchumann (talk) 02:16, 21 June 2008 (UTC)


 * I have added participation and consistency to the table. Markus Schulze 10:43, 21 June 2008 (UTC)

Path heuristic implementation

 * Is the code in the path heuristic "Implementation" section pseudocode or an actual programming language? -- Explodicle (T/C) 16:52, 9 July 2008 (UTC)
 * It is Pascal-like pseudocode. Markus Schulze 18:57, 9 July 2008 (UTC)


 * Will the casual audience actually go over the code? Can we put it in a template? -- Explodicle  (T/C) 16:52, 9 July 2008 (UTC)
 * In my opinion, the template confuses inexperienced readers too much. Therefore, it should be used only when the article would become too long otherwise. Markus Schulze 18:57, 9 July 2008 (UTC)

Ranking?
Could somebody please add an example of how the Schulze method creates a ranking (as stated in the intro) instead of just determining a single winner? Thanx. 88.73.116.159 (talk) 20:09, 21 October 2008 (UTC)


 * Done. Markus Schulze 21:31, 21 October 2008 (UTC)

Referencing
The article as it stands has multiple referencing problems - I have marked some of them with the tag, and added a  to the top of the whole article. DuncanHill (talk) 10:24, 31 July 2008 (UTC)

Later-no-harm criterion
I removed the later-no-harm criterion from the comparison table because of the following reasons: In my opinion, all these problems of the later-no-harm criterion should be highlighted at the later-no-harm criterion article and not at the Schulze method article. Markus Schulze 17:57, 1 October 2008 (UTC)
 * 1) The later-no-harm criterion isn't sufficiently well defined. It is rather a paradigm than a proper criterion. For example: Does the Coombs' method satisfy this criterion? Does anti-plurality satisfy this criterion? Does plurality satisfy this criterion?
 * 2) Whether a given election method satisfies later-no-harm depends too much on the details of this method. For example: User:70.255.172.161 mentions that, when pairwise opposition is used as a measure for the strength of a pairwise defeat, then MinMax satisfies later-no-harm; but to be fair, you would then also have to mention that, when pairwise opposition is used as a measure for the strength of a pairwise defeat, then MinMax violates the Condorcet criterion; but to be fair, you would then also have to mention that, when pairwise opposition is used as a measure for the strength of a pairwise defeat, then also the Schulze method violates the Condorcet criterion; etc..

I disagree with the removal. Most methods list later-no-harm in their list of satisfied/unsatisfied criteria on their own article page. If its inclusion is inappropriate in the chart then its inclusion is inappropriate in the article pages. I think standard implementations should apply to the chart, not possible variations. MiniMax, as per your example, doesn't specify a typical implementation therefore 'Depends' was an appropriate response (barring three separate MiniMax entries). --129.115.251.22 (talk) 00:22, 2 October 2008 (UTC)

At least for 6 of the 15 methods, that are listed in the comparison table, it is disputed whether this method satisfies the later-no-harm criterion: It is disputed for Coombs' method and for anti-plurality voting, because it isn't clear how these methods are defined for incomplete individual rankings. It is disputed for plurality voting, supplementary voting, and Sri Lankan contingent voting, because it is disputed whether the later-no-harm criterion can be applied to election methods that restrict the number of cast preferences. It is disputed for the MinMax method, because the typical implementation of this method is disputed.

Adding the later-no-harm criterion to the comparison table would move the discussion of this criterion from Talk:Later-no-harm criterion to the Schulze method article. Markus Schulze 01:38, 2 October 2008 (UTC)


 * Later-no-harm actually is not disputed for plurality voting and anti-plurality voting. Neither system is preferential so later-no-harm is inapplicable (not a yes or no).  The only real dispute is with MiniMax since its definition of score can change its satisfied criteria.  The others are just unknown at this point. Tastywheat (talk - contribs) 14:43, 2 October 2008 (UTC)


 * (1) It is disputed whether plurality voting satisfies later-no-harm. For example, Woodall argues that plurality voting satisfies later-no-harm . (2) You wrote: "The only real dispute is with MiniMax since its definition of score can change its satisfied criteria." Well, also whether e.g. the Borda count satisfies later-no-harm depends on its definition of score. (3) Furthermore, it is disputed whether the Coombs' method satisfies later-no-harm, since usually this method is defined only for complete individual rankings. Markus Schulze 16:15, 2 October 2008 (UTC)

understandable?
I don't want to edit it without discussion, but wouldn't a column on the comparison chart that indicates whether a voting method can be explained to an uneducated person in a few sentences. while the Schulze method seems clearly to be the best method, it certainly couldn't be introduced to many americans without saying "don't worry about it, We educated few have ensured that this is the fairest method." instant runoff seems to have an advantage in this while still being hugely more fair than our current method. —Preceding unsigned comment added by 216.73.248.58 (talk) 15:44, 28 October 2008 (UTC)


 * There is a difference between the question whether a method is understandable on the one side and e.g. the question whether a method satisfies monotonicity, clone independence or reversal symmetry on the other side. The difference is: Every reader can easily make his own opinion about how understandable a method is; so he doesn't really need someone else to answer this question for him. On the other side, it is not clear at first glance whether a method satisfies monotonicity, clone independence or reversal symmetry; thorough mathematical investigations are needed to answer this question; so for this question, the comparison chart is really helpful to the reader. Markus Schulze 19:25, 28 October 2008 (UTC)


 * I see. But what of the question of simplicity in a method. No method can be implemented in politics that can't be easily understood and so methods like the Schulze method are not useful for politics. right?


 * Wikipedia is an encyclopedia and not a discussion forum. So the claim, that "the Schulze method is not useful for politics", does not belong to a Wikipedia article. Rather this article should give each reader the opportunity to make his own opinion about this method. Markus Schulze 22:20, 3 November 2008 (UTC)

Whenever some more complex method of voting is suggested for use in real life, such objection is often heard. Granted this is a more tehnical article, but if its scope might include such things like, say pros and cons, such issue might be incorporated in wiki fashion. There is some discussion of this kind in MMP article for example. It would not be a bad idea that it is answered to in such manner, for I believe its easily answerable, for many democracies in the world, eg. any country that uses for eg. proportional representation, use a calculation method that generally doesn't interest the public, for achieving proportionality. I learned how my elections are calculated exactly (and that's just a simple D'Hondt) practically by accident, in college, and most people have no idea. Getting the basic idea what its supposed to do, how one affects the outcomes with the vote is important, but exact calculation methods are rather frequently something esoteric and uninteresting to the public in many democracies. —Preceding unsigned comment added by 93.136.58.60 (talk) 04:36, 28 May 2009 (UTC)

schulze stv
I don't see information on how this method relates to the Schulze STV method.


 * The article on the Schulze STV method says: "When two results differ by more than one candidate, a path must be determined that leads from one result to the other. The strength of a path is equal to the weakest link along the path." This is exactly the same as saying that the Schulze method is applied to a digraph where each vertex represents a possible winning set. Markus Schulze 00:41, 31 October 2008 (UTC)


 * I would like to see a layman(me)-understandable textual description (and comparison) of the differences/similarities/improvements between the 'Schulze' in this method and the 'Schulze' in the Schulze STV method, even if it's just a sentence. If they're rather different but share your name in part, I'd just like it to be clear that the name doesn't indicate that they're mostly identical or that one is a derivation of the other.


 * The Schulze STV method is a generalization of the Schulze method from single-winner election methods to proportional representation by the single transferable vote. So when there is only one seat, then the Schulze method and the Schulze STV method are identical. Markus Schulze 23:40, 5 November 2008 (UTC)

Explanation
Could someone write an explanation section which would makes sense to poor saps like me who have to use it? The article as it stands is incomprehensible. It would be nice to have some idea of who this Schulze person is too. DuncanHill (talk) 18:13, 28 June 2008 (UTC)
 * Obviously not. DuncanHill (talk) 12:07, 15 December 2008 (UTC)
 * Did you try the examples? Markus Schulze 15:19, 15 December 2008 (UTC)
 * Yes. With respect Markus, I think the article really needs a thorough going over by someone who a) understands the system, and b) isn't as close to it as you are. You've obviously put a huge amount of work both into developing the system and writing the article, I just think that for the more general reader a less involved editor might be able to express things more clearly. That is, things which seem very clear to you, because you have pondered them and worked on them for a long time, won't always seem clear to people who are coming to the article to find out about it for the first time. DuncanHill (talk) 15:57, 15 December 2008 (UTC)
 * agree!! it must be rewritten for everyone --83.57.188.243 (talk) 18:21, 30 July 2009 (UTC)

Schwartz heuristic example
I'm trying to figure out how this method works. Following the example, C comes out as winner. But if I did the pairwise comparisons correct, I cannot understand how is C a better candidate than A. A beats B 16:14 and C 17:13, losing to D 12:18. C loses to A, and to B 11:19, but wins D 20:10. So, whats the rationale and criteria used to conclude C is a better winner? It looks to me that A loses by both a smaller margins (-6, while C lost by -4 and -8) and wins more often (by 2 and by 4, as opposed to a win by 10) ? —Preceding unsigned comment added by 93.136.58.60 (talk) 04:19, 28 May 2009 (UTC)


 * The justification for the Schulze method is that it satisfies a large number of academic criteria (e.g. monotonicity, mutual majority, independence of clones, reversal symmetry, Pareto). By the way: The strength of the strongest path from candidate C to candidate A is p[C,A] = 18, while the strength of the strongest path from candidate A to candidate C is p[A,C] = 17. Markus Schulze 07:58, 28 May 2009 (UTC)
 * Oh, so I did miscount, thx for the explanation :) I understand its theoretical appeal, I was asking about that specific example. Well, a simple error on my part explains it it seems :) —Preceding unsigned comment added by 93.139.125.85 (talk) 09:20, 28 May 2009 (UTC)

Reinforcement
Does the Schulze method meet the criterion named reinforcement? This criterion is missing from the list of satisfied and failed criteria. Specifically, if ballots are divided into two (or more) separate races and the ranking of candidates (who is first, who is second, etc.) for the separate races are the same, then does the Schulze method identify the same ranking when all the ballots are combined into a single race? VoteFair (talk) 18:52, 4 July 2009 (UTC)
 * The Schulze method doesn't satisfy the reinforcement criterion. Markus Schulze 01:16, 5 July 2009 (UTC)

Far too many references
There are too many references in this articles. Maybe one tenth of what is here would be sufficient. More than that means that this article is becoming essentially an archive for references. This is not NPOV. --Pot (talk) 01:00, 24 April 2010 (UTC)
 * I found the references relevant and useful for the most part; at least as it is now (months after the original post). There is nothing POV about being comprehensive. Le kasydzu (talk) 07:12, 6 October 2010 (UTC)

Indifference between candidates
Great article. I would like to see at least one example where voters prefer some candidates equally. IE: 'A>B=C>D=E'. Thanks. —Preceding unsigned comment added by 98.202.77.37 (talk) 20:01, 22 March 2009 (UTC)

Furthermore, it would be good if the article gave some examples where the value of d[V,W] + d[W,V] is not the same for all candidate pairs. I.e. with 50 voters, how does a 26-24 win compare to a 10-0 win with 40 voters putting these candidates as equal? DavidNorman99 (talk) 23:12, 3 October 2010 (UTC)


 * I agree. This article should contain some more examples. Originally, this article contained 4 examples. However, the other 3 examples have been removed here and again here. Markus Schulze 15:52, 4 October 2010 (UTC)


 * I agree too. This method seems to have major problems when you have large numbers of candidates because the linear ordering will force distances into your list that you didn't want. I added an example below about crackpots vs. established candidates. —Preceding unsigned comment added by 173.79.213.161 (talk) 15:43, 5 November 2010 (UTC)

Later-no-harm
Why is Later-no-harm criterion not included in the comparison table with other systems? Somnolentsurfer (talk) 22:06, 12 March 2011 (UTC)


 * Anti-plurality and Coombs are defined only for complete individual rankings. Whether MiniMax satisfies later-no-harm, depends on the details of this method. Markus Schulze 23:33, 12 March 2011 (UTC)

Doesn't this method favor kooks/crackpots?
Suppose you have an established candidate E and crackpots C1, C2, C3, and C4. Half the people want the established candidate, and the other half want a crackpot.

The problem with the method is that it is very difficult for supporters of the established candidate to vote against all the crackpots. If they're not careful, they might vote like this:
 * 49: E>C1>C2>C3>C4
 * 18: C1>C2>C3>C4>E
 * 17: C2>C1>C3>C4>E
 * 16: C3>C1>C2>C4>E

and C1 wins.

The crackpot supporters have an inherent advantage because they know who to vote against. —Preceding unsigned comment added by 173.79.213.161 (talk) 15:33, 5 November 2010 (UTC)
 * The purpose of this page is to discuss improvements to the article. It is not a debate forum on the general topic of the Schulze method. See WP:TALK and WP:NOTAFORUM. Gabbe (talk) 15:37, 5 November 2010 (UTC)
 * Candidate C1 is a Condorcet candidate. Therefore, this is rather a criticism of Condorcet methods in general than a criticism of the Schulze method in particular. Actually, many election methods would choose candidate C1. And except for the fact that you call candidate C1 a "kook" and "crackpot", I see no reason why candidate C1 shouldn't be elected. Markus Schulze 16:17, 5 November 2010 (UTC)
 * Right, it might as well be E=Republican, C1=Centrist(Blue dog)-Democrat, C2=Traditional-Democrat, C3=Green-Democrat. Tom Ruen (talk) 04:53, 28 November 2010 (UTC)

To further extend this, C1 would be elected under the following methods:

Baldwin, Black, Borda, Bucklin, Coombs, Copeland, Dodgson, Nanson, Simpson, Small

Depending on the tiebreaker, the following would also chose C1 as the winner:

Hare (Instant Runoff), Raynaud, Tideman, and a traditional two round system runoff.

Whether or not C1 is a crackpot, a great many election methods pick that candidate as the winner. If people are more likely to prefer a good candidate over a bad candidate, it's more likely that E would be the crackpot.

To go back to an earlier post, it would be nice to add Reinforcement to the table of criteria. —Preceding unsigned comment added by 184.100.13.107 (talk) 03:25, 28 November 2010 (UTC)


 * The problem with the reinforcement criterion is that this criterion is defined only for those election methods that always create a complete ranking of all candidates. Markus Schulze 12:09, 28 November 2010 (UTC)

Continuing the clean-up
I have tried to clean up the introduction and definition. This article, like many other on election methods, has most of its "volume" taken up by really long examples, which I did not touch. I would suggest to have one small example with more detail, and possibly one larger example with less detail.

I renamed the two sections to "implementations", but I did not look at them in detail. Can the second one be simply deleted or moved to another page? I don't see any benefit to including it, and it doesn't explain any motivation. Is it a "heuristic" that only works some times, or does it always give the same answer? I don't see why anyone would care about running a different algorithm to execute the Schwarz method, given that the original definition is essentially already by a very straightforward algorithm.

If someone would re-write or clean up the example/implementation sections, I think you could take away the "confusing" warning on the page.

As an aside: there are some technical points which aren't covered on the page: Daveagp (talk) 17:35, 24 April 2011 (UTC)
 * the outcome of the voting mechanism depends on how you 'score' voter ties. For example, if everyone is indifferent between A and B, you might either set d[A, B]=d[B, A]=0 or d[A, B]=d[B, A]=n/2 where n is the number of voters, but these would give different results. Given that the Schulze method is promoted since it has good properties, it would make sense to clarify whether there is any pro/con to one choice or the other.
 * the outcome of the mechanism gives only quasi-transitive preferences. For example, two voters A>B>C>D and C>D>A>B leads to the output A>B, C>D, and D=A=C=B=D.
 * if this page is used as a reference description for elections like in Wikimedia, it's very important that the first thing is specified, and also the second thing to be specified is what is done when there is no strict winner

Further (Daveagp (talk) 16:51, 27 April 2011 (UTC)) I deleted the "research papers" since it was just a long list, with several out-of-date/borderline irrelevant links and I think scholar.google back-reference searches would be better for finding this list. The list of books/surveys may not be appropriate either unless they serve a specific purpose, but shouldn't wikipedia itself have enough of a well-written article not to need to point readers elsewhere?


 * Concerning the fact that you get more than 100 scholar.google hits for "Schulze method", it makes sense to give a short list of some research papers. Markus Schulze 17:50, 27 April 2011 (UTC)


 * If you think they are important, then it would make sense to me to include them as references in a section titled "Research" summarizing the research... I have removed them again because Wikipedia is not a directory. --Izno (talk) 20:48, 27 April 2011 (UTC)

Thanks for your feedback. I had some more energy to rewrite all the parts which I thought were muddled. Like Izno I think adding individual references is valuable if and only if they are accompanied by an explanation of why they are significant. Daveagp (talk) 12:09, 11 May 2011 (UTC)

The Lakehead v Thunder Bay
I find this article a bit confusing. The Lakehead beats Thunder Bay in the head to head. So should "Thunder Bay --(23679)--> The Lakehead" be the other way round? Bejjer (talk) 13:39, 13 July 2011 (UTC)

Clarification question
Firstly this article, defines some if it's terms (such as P), by the terms themselves, which is difficult to understand.

Secondly, help me elucidate something.

if 45 people voted for 5 candidates {a,b,c,d,e}, marking them by ordered preference {1..5}, then why all this redundant math? Is it not the same as summing up the score per candidate and finding out that E has won...?

This is equivalent to each voter having 15 (=1+2+3+4+5) points to spread across 5 candidates, sum each candidate score (no graphs needed), and get the ordered list the voters created. what's the advantage of these extra steps ? what's the motivation, and what do they reveal? getting a single winner out of the 5 can be done much simpler.-- Namaste@ ? 15:17, 8 November 2011 (UTC)


 * The method, you are talking about, is the Borda count. The Borda count violates the majority criterion and the independence of clones criterion. Markus Schulze 19:26, 8 November 2011 (UTC)

Comparison table
I am willing to put more columns in the comparison table, "resolvability", "MinMax set" and "prudence". Resolvability was mainly because I added Copeland to the table. MinMax because it is the main difference between Schulze and ranked pairs. Prudence is also in Schulze's paper, which I am using as source. --Wat 20

But I don´t know the row values for all the methods. Is there a problem if I leave some of them blank? --Wat 20


 * (We can't tell who wrote the above unsigned comment. Was it Markus?)
 * The comment above and the article refer to a "main" difference between Schulze and Ranked Pairs. Is this just a point of view? If so, the word "main" should be deleted from the article. The difference that I would deem "main" is that more voters will rank Ranked Pairs winners over Schulze winners than vice versa, over the long run. Similarly, majorities will rank Ranked Pairs winners over Schulze winners more often than vice versa. (These results were established by computer simulations in which thousands of collections of randomly generated voters' orders of preference were tallied by both methods. The results were confirmed independently by Norm Petry in the Election-Methods mailing list, and to the best of my knowledge were never challenged by Markus.) SEppley (talk) 18:28, 13 March 2012 (UTC)


 * I referred as "main" above, because it is the only difference documented in Schulze paper. And I´m not the one who wrote "main" in the article. IMHO additional columns in the comparison table and separate criterion articles are a more objective approach than descriptions in the bottom of that same table. All the explanations/criticisms here in the discussion page could have been in a dedicated MinMax criterion article. --Wat 20 18:48, 24 May 2012 (UTC).


 * In fact, the history can tell who wrote the above unsigned comment. The author was "Wat 20" (date: 2011-12-16). --Arno Nymus (talk) 05:10, 14 March 2012 (UTC)


 * The mentioned computer simulations also confirmed that the worst pairwise defeat of the ranked pairs winner is almost always worse than the worst pairwise defeat of the Schulze winner. To the best of my knowledge, this result was never challenged by Steve Eppley. Markus Schulze 07:31, 14 March 2012 (UTC)


 * That can't be true, since the simulations showed that both methods usually elect the same winner. Assuming Markus meant only the scenarios in which the two methods elect different winners, at most one of the two mentioned simulations could have confirmed it since my simulations didn't test for it. I don't know if Norm Petry's simulations confirmed it or not. (Have a url?) True or not, no one has not provided an argument why that should be considered the "main" difference between the two methods; to do so, one would need to explain why it's more important than that more voters will rank Ranked Pairs winners over Schulze winners than vice versa over the long run, why it's more important than that majorities will rank Ranked Pairs winners over Schulze winners more often than vice versa (results which Markus has now implicitly acknowledged here by his absence of challenge), why it's more important than Local Independence of Irrelevant Alternatives, why it's more important than Immunity from Majority Complaints, etc. It seems to be just someone's point of view, so it should not be called the "main difference" in the article. SEppley (talk) 23:24, 14 March 2012 (UTC)


 * Please read the calculations by Norman Petry, Jobst Heitzig, and Barry Wright. Markus Schulze 08:03, 15 March 2012 (UTC)


 * Those citations do not confirm Markus' claim. They do not compare the sizes of reversed majorities; they only compare whether methods pick the same winner. They show Ranked Pairs and Schulze usually pick the same winner, which means the claim by Markus above, taken literally, is wrong. They also say the winners of Schulze's method are more often the same as the winners of some voting methods (e.g., MinMax) that Markus obviously believes are inferior to the Schulze method (and I agree they're inferior). But the similarity of B to B2 doesn't imply B is superior to A. (If one thinks it does, then by similar reasoning one should prefer the Borda method since it too judges superiority based on similarity to other inferior alternatives. See the Borda example in the independence of clones article.)


 * Barry Wright's paper used Tideman's version of Ranked Pairs, which calculates sizes of majorities by subtracting sizes of their opposing minorities, and Wright doesn't indicate whether his simulated votes can include indifference. So let's assume indifferences, if any, rarely cause the two variations of Ranked Pairs to differ when votes are random, so that Wright's data apply to both. (There will continue to be a disambiguation problem if people continue to use the name Ranked Pairs for both.)


 * Wright's paper fudges where he claims MinMax is independent of clones. He substitutes a weaker concept he calls "internal" clones, which are clones that tie each other pairwise. (Pairwise ties won't change any candidate's largest pairwise defeat.) Clones will rarely be "internal" so if Wright is trying to make a point, it's that a minority might have trouble exploiting MinMax's vulnerability to clone nominations. If we assume would-be manipulators will have trouble predicting voters' preferences between similar alternatives that cycle, then perhaps a revealing case to simulate is where voters randomly express strict preferences between similar alternatives, to answer the following: What is the chance of a "vicious" cycle (in which every clone's largest pairwise defeat is to another clone, changing the winner to a candidate they all defeat pairwise by a significant majority)? Does the chance increase as the number of clones increases, or is at least one of the clones likely to not have its largest pairwise defeat grow as the number of clones increases?


 * Here's a link to my webpage containing the data from the computer simulations I mentioned above, which compare voters' preferences for Schulze winners versus Ranked Pairs winners. (By which I mean the "winning votes" variation of Ranked Pairs. To be precise, my Maximize Affirmed Majorities variation, which differs in three ways from Tideman-Zavist's "margins" variation.) This direct comparison of the two methods, which shows more voters will prefer Ranked Pairs winners, seems more consistent with the spirit of Arrow's IIA than does Markus' comparison, since Markus' comparison is about third (or fourth) candidates. SEppley (talk) 15:44, 15 March 2012 (UTC)

Here are Norman Petry's calculations:

A: number of candidates B: SmithMinMax = Tideman = Schulze C: SmithMinMax = Schulze <> Tideman D: Tideman = Schulze <> SmithMinMax E: SmithMinMax <> Tideman <> Schulze <> SmithMinMax F: SmithMinMax = Tideman <> Schulze

So when there are e.g. 15 candidates, then in 45.47% ( = 41.22% + 4.25% ) of all cases, the MinMax scores of the Schulze winner and the Tideman winner are identical. In at least 50.46% of all cases, the Schulze winner has a better MinMax score than the Tideman winner. In at least 0.62% of all cases, the Tideman winner has a better MinMax score than the Schulze winner. In the remaining 3.45%, the simulations are unclear. But even if we presume that in all the remaining 3.45% the Tideman winner has a better MinMax score than the Schulze winner, Norman Petry's simulations clearly show that the number of cases, where the Schulze winner has a better MinMax score than the Tideman winner, outweights by far the number of cases, where the Tideman winner has a better MinMax score than the Schulze winner. Markus Schulze 08:57, 16 March 2012 (UTC)

Unclear description of "set with minimum MinMax score."
The article refers to "the set with minimum MinMax score." Can this be rewritten for greater clarity? Consider the set that contains only the candidate that would be elected by the MinMax method. Why isn't this the set that has the minimum MinMax score? (The Schulze method doesn't necessarily elect the MinMax winner.) SEppley (talk) 18:37, 13 March 2012 (UTC)


 * See section 4.8 of my paper. Markus Schulze 08:30, 15 April 2012 (UTC)

Disputed content.
I removed some content. Content that looked like a instruction manual. User:MarkusSchulze(WP:COI) reverted without explanation. Could someone explain me why that should not be removed?--Müdigkeit (talk) 09:11, 17 October 2012 (UTC)
 * Well, an election method is an instruction set. Therefore, it doesn't make much sense to quote a Wikipedia policy that says that an article must not contain an instruction set. Markus Schulze 09:40, 17 October 2012 (UTC)

Edits by User:Müdigkeit
User:Müdigkeit has removed large parts of this article claiming that it violated Wikipedia's policy on first person usage. However, Wikipedia's policy on first person usage says:


 * Articles should generally not be written from a first or second person perspective. In prose writing, the first person ("I" and "we") point of view and second person ("you" and "your") point of view typically evoke a strong narrator. While this is acceptable in works of fiction, it is generally unsuitable in an encyclopedia, where the writer should be invisible to the reader.  Moreover, pertaining specifically to Wikipedia's policies, the first person often inappropriately implies a point of view inconsistent with WP:NPOV, and second person is inappropriately associated with step-by-step instructions of a how-to guide (see WP:NOTHOWTO).  First and second person pronouns should ordinarily be used only in attributed direct quotations relevant to the subject of the article.  As with many such guidelines, however, there are exceptions: for instance, in professional mathematics writing, use of the first person plural ("we") as "inclusive we" is widespread.

Markus Schulze 14:28, 17 October 2012 (UTC)
 * First of all:That is not a policy, that is an essay! Even if it is used in professional mathematics writing, that does not mean that it is right to use here. The tone of Wikipedia should always be encyclopedic. And the first person is not encyclopedic, except for quotations. This article is not to be read just by experts.
 * Second of all: A large part of it was the removal of external links, which were excessive. I will remove them a second time because you did not say anything against that. --Müdigkeit (talk) 14:56, 17 October 2012 (UTC)
 * I did not remove large parts of text because of the "we". I just rephrased these parts which, as written in the Manual of Style, is often better.--Müdigkeit (talk) 15:15, 17 October 2012 (UTC)

More edits by User:Müdigkeit
The recent edits by User:Müdigkeit are clearly POV-motivated. There are similar articles with similar numbers of items in their external links sections. For example, the instant-runoff voting has 31 items in its external links section; the single transferable vote article has 38 items in its external links section; the Borda count article has 23 items in its external links section. Markus Schulze 19:52, 17 October 2012 (UTC)
 * WP:LINKFARM. Just because another article does not follow policy does not imply that this one should not. Also, you have WP:COI as well, so be careful with claims that one person or another is driven by a certain motivation. WP:OWN is also a policy; you are not the only one to decide. --Izno (talk) 23:35, 17 October 2012 (UTC)
 * Well, I will look if the other articles have too much external links, but remember: A similar article is not the same article. If might be appropiate there and not here, or it might be inappropiate here and there...--Müdigkeit (talk) 05:48, 18 October 2012 (UTC)

WP:COI
I do not have a conflict of interest here. My only interest for editing this article is improving Wikipedia.--Müdigkeit (talk) 05:34, 18 October 2012 (UTC)

Too complex
Hello! I don't understand this article. There's too much code and the example is too complex, so I don't understand how the system works. In contrast, Ranked pairs is very simple to understand. Can you fix the article? Thanks! --NaBUru38 (talk) 17:04, 9 November 2012 (UTC)


 * Example 1 (section 3.1) of my paper is simpler and more detailed. Markus Schulze 08:10, 10 November 2012 (UTC)

Adding &lt; math &gt; to formulae
I took the liberty (please don't bite me) of adding &lt; math &gt; around all the formulae I could find. Any thoughts? Obviously there is room for interpretation, such as mathing (just verbed the word math) single variables and mathing in tables. Thanks

71.182.149.159 (talk) 02:26, 21 January 2013 (UTC) (applying for an account, sorry)

Correctness of pseudocode
Is the article's pseudocode for computing strongest path strengths in fact correct? While not stated explicitly, the pseudocode appears to be using the winning votes metric for measuring strength. Schulze's paper lists the conditions for "stronger than" under winning-votes as follows (my paraphrasing):


 * 1) A win is stronger than a loss or a tie.
 * 2) A tie is stronger than a loss.
 * 3) A landslide victory is stronger than a narrow victory.
 * 4) A victory with weak opposition is stronger than an equal victory with strong opposition.

Because the article's pseudocode first computes each pair's support ($N[e,f]$ in the paper's notation) then iteratively applies straight min and max to pairs of those, doesn't this miss condition 4? For example, if there are 10 votes for $A>B$, 2 votes for $B>A$, 10 votes for $C>D$, and 8 votes for $D>C$, then Schulze's definition indicates that the $A>B$ win is stronger than the $C>D$ win, but the pseudocode treats them as equal.

Scott Pakin (talk) 17:23, 15 September 2013 (UTC)

Doesn't "cloneproof" make a difference?
In the lead, it's claimed that: "The Schulze method is also known as Schwartz Sequential Dropping (SSD), Cloneproof Schwartz Sequential Dropping (CSSD), [...]"

However, I'm given to understand that there is a difference between SSD and CSSD (see e.g. SSD and CSSD Condorcet), so it seems somewhat deceptive (if unintentionally so) to say the above without qualification. &mdash;SamB (talk) 22:56, 27 June 2015 (UTC)


 * The Schulze method has two degrees of freedom: (1) How do you define the strength of the link from candidate X to candidate Y? (2) When there is more than one candidate D with p[D,E] &ge; p[E,D] for every other candidate E, then how do you choose the final winner from amongst these candidates? The terms "Schwartz Sequential Dropping" (SSD) and "Cloneproof Schwartz Sequential Dropping" (CSSD) refer to different answers to the second question.
 * By the way, the Schulze method is resolvable. This means that when the number of voters is large then the probability that there is more than one candidate D with p[D,E] &ge; p[E,D] for every other candidate E goes to zero. Markus Schulze 05:49, 28 June 2015 (UTC)

As a neutral party, I'd like to object to the "This article may contain an excessive amount of intricate detail that may only interest a specific audience." critque
I came to this article because this method is going to be used for a vote that I'm participating in. Yes, the article is detailed, but I found it to be the right level of detail to both understand what is going on and even to implement the system if I wanted to validate the election myself. Anyone interested in this style of voting because it impacts them seems likely to need this.

Now, having said that -- even though I wouldn't remove any content (and therefore I support removing the critique), I would reorder the content. What I would suggest is that the EXAMPLE section should move up before any of the technical details of computation. That's the most accessible information and should be first. I would also make the intro much more of a soft landing, something like:

''This is an alternate voting system. It is meant to evaluate ballots where voters rank a bunch of items to find the highest ranked item that will make the most voters happy. It produces a ranked list of candidates, so evaluating second place, third place, etc, is easy. It accounts for the possibility that some voters might not rank some items because they do not know or do not care about them. The Schulze method is also known as Schwartz Sequential Dropping (SSD), Cloneproof Schwartz Sequential Dropping (CSSD), the Beatpath Method, Beatpath Winner, Path Voting, and Path Winner.''

I would move all the rest down into the details. — Preceding unsigned comment added by AristosM (talk • contribs) 06:42, 5 February 2014 (UTC)


 * The section "Computation" is part of the definition of the Schulze method. You cannot give an example before you have given a definition. Markus Schulze 07:46, 7 February 2014 (UTC)


 * What's stopping us from giving an example before giving the definition, exactly? &mdash;SamB (talk) 18:53, 27 June 2015 (UTC)


 * I don't understand your question. Could you please refer to an article on an election method where an example is given before the definition is given? Markus Schulze 05:55, 28 June 2015 (UTC)

Totally incomprehensible to people, use the "Tennessee example" to explain
See the pages for plurality voting and instant runoff voting if you want to see how it's done, Mr. Schulze.


 * The "Tennessee example" has a Condorcet winner. However, to explain a concrete Condorcet method, you have to use an example without a Condorcet winner. Otherwise, the difference between e.g. the Schulze method, ranked pairs, and the Kemeny–Young method wouldn't be clear. Markus Schulze 07:26, 4 August 2015 (UTC)

Users
I removed the table of users. It is too difficult to find a reasonable and objective classification for private organizations. For example: Kingman Hall, Technology House, and Hillegass Parker House are student housing cooperatives. But Kingman Hall is classified as an "academic organization"; Technology House is classified as a "technology organization"; and Hillegass Parker House is classified as "other use". Markus Schulze 19:24, 26 October 2015 (UTC)

Possible error in the Algorithm
When I run the algorithm on the page, I get the strength of the strongest path of 23 not 25 going from C to A. Looking at the code, I can see where it gets 23 from. The "path" from the algorithm is the equivalent of [(C,B),(B,D),(D,C),(C,E),(E,A)]. The corresponding weights are [29,33,28,24,23]. 23 is the minimum of the weights. The algorithm made an illegal move going from D to C. C is a visited node and it creates a [(C,B),(B,D),(D,C)] cycle. Please tell me if I am wrong. Would a better algorithm be a DFS algorithm with max weights as a selection criteria? In that case, it can be solved in $$O(n \log n)$$ time. Much better than the posted $$O(n^3)$$ time. Another possible error I see is in the example going from B to A. Should this be 23 not 25? I get the path [(B,D),(D,C),(C,E),(E,A)]? The corresponding weights are [33,28,24,23]. The lowest is 23. Why pick A over D when D clearly has the largest weight?


 * You wrote: "Another possible error I see is in the example going from B to A. Should this be 23 not 25? I get the path [(B,D),(D,C),(C,E),(E,A)]? The corresponding weights are [33,28,24,23]. The lowest is 23. Why pick A over D when D clearly has the largest weight?" The weakest link of the path B- (25) -A has a strength of 25. The weakest link of the path B-(33)-D-(28)-C-(24)-E- (23) -A has a strength of 23. Therefore, the path B- (25) -A is stronger than the path B-(33)-D-(28)-C-(24)-E- (23) -A.


 * The path B- (25) -A consists only of the direct link from B to A. As the described algorithm starts with direct links as paths ( p[i,j] := d[i,j] ) and updates a path only when it has found a shortcut ( p[j,k] := max ( p[j,k], min ( p[j,i], p[i,k] ) ) ), I don't see how this algorithm could give B-(33)-D-(28)-C-(24)-E- (23) -A as strongest path. Markus Schulze 08:11, 28 December 2015 (UTC)


 * When you implement the Floyd–Warshall algorithm, the order of the indices is very important. Only when you consider the possible shortcuts in that very special order, it is guaranteed that a single pass through the triple-loop is sufficient to find all shortest paths. I have checked the Floyd–Warshall algorithm manually for the example; it gives correct results. Markus Schulze 08:29, 29 December 2015 (UTC)


 * Here is a documentation of the Floyd–Warshall algorithm. We start with


 * p[A,B]=0;


 * p[A,C]=26;


 * p[A,D]=30;


 * p[A,E]=0;


 * p[B,A]=25;


 * p[B,C]=0;


 * p[B,D]=33;


 * p[B,E]=0;


 * p[C,A]=0;


 * p[C,B]=29;


 * p[C,D]=0;


 * p[C,E]=24;


 * p[D,A]=0;


 * p[D,B]=0;


 * p[D,C]=28;


 * p[D,E]=0;


 * p[E,A]=23;


 * p[E,B]=27;


 * p[E,C]=0;


 * p[E,D]=31;


 * {| class="wikitable" style="text-align:center"

! stage !! i !! j !! k !! p[j,k] !! p[j,i] !! p[i,k] !! result !1||A||B||C||0||25||26||p[B,C] is updated from 0 to 25 !2||A||B||D||33||25||30|| !3||A||B||E||0||25||0|| !4||A||C||B||29||0||0|| !5||A||C||D||0||0||30|| !6||A||C||E||24||0||0|| !7||A||D||B||0||0||0|| !8||A||D||C||28||0||26|| !9||A||D||E||0||0||0|| !10||A||E||B||27||23||0|| !11||A||E||C||0||23||26||p[E,C] is updated from 0 to 23 !12||A||E||D||31||23||30|| !13||B||A||C||26||0||25|| !14||B||A||D||30||0||33|| !15||B||A||E||0||0||0|| !16||B||C||A||0||29||25||p[C,A] is updated from 0 to 25 !17||B||C||D||0||29||33||p[C,D] is updated from 0 to 29 !18||B||C||E||24||29||0|| !19||B||D||A||0||0||25|| !20||B||D||C||28||0||25|| !21||B||D||E||0||0||0|| !22||B||E||A||23||27||25||p[E,A] is updated from 23 to 25 !23||B||E||C||23||27||25||p[E,C] is updated from 23 to 25 !24||B||E||D||31||27||33|| !25||C||A||B||0||26||29||p[A,B] is updated from 0 to 26 !26||C||A||D||30||26||29|| !27||C||A||E||0||26||24||p[A,E] is updated from 0 to 24 !28||C||B||A||25||25||25|| !29||C||B||D||33||25||29|| !30||C||B||E||0||25||24||p[B,E] is updated from 0 to 24 !31||C||D||A||0||28||25||p[D,A] is updated from 0 to 25 !32||C||D||B||0||28||29||p[D,B] is updated from 0 to 28 !33||C||D||E||0||28||24||p[D,E] is updated from 0 to 24 !34||C||E||A||25||25||25|| !35||C||E||B||27||25||29|| !36||C||E||D||31||25||29|| !37||D||A||B||26||30||28||p[A,B] is updated from 26 to 28 !38||D||A||C||26||30||28||p[A,C] is updated from 26 to 28 !39||D||A||E||24||30||24|| !40||D||B||A||25||33||25|| !41||D||B||C||25||33||28||p[B,C] is updated from 25 to 28 !42||D||B||E||24||33||24|| !43||D||C||A||25||29||25|| !44||D||C||B||29||29||28|| !45||D||C||E||24||29||24|| !46||D||E||A||25||31||25|| !47||D||E||B||27||31||28||p[E,B] is updated from 27 to 28 !48||D||E||C||25||31||28||p[E,C] is updated from 25 to 28 !49||E||A||B||28||24||28|| !50||E||A||C||28||24||28|| !51||E||A||D||30||24||31|| !52||E||B||A||25||24||25|| !53||E||B||C||28||24||28|| !54||E||B||D||33||24||31|| !55||E||C||A||25||24||25|| !56||E||C||B||29||24||28|| !57||E||C||D||29||24||31|| !58||E||D||A||25||24||25|| !59||E||D||B||28||24||28|| !60||E||D||C||28||24||28||
 * }
 * Markus Schulze 13:08, 29 December 2015 (UTC)

This cleared everything up. I didn't consider order of indicies. Thanks so much for your response!!!

Suggest Adding Later-No-Help and Later No-Harm (in comparison table)
It seems to me that Later-No-Help and Later-No-Harm should be added to the compliance table.

My reasoning: If these criteria were not important then a three-candidate election would be trivially solvable, but it is not.

We could omit LNH if we were only comparing Condorcet methods that all failed, for the purpose of identifying the differences between the Condorcet methods. But, if we are also comparing to plurality elimination systems (i.e. sequential runoff systems) such as IRV then we must include LNH Harm/Help (in the comparison table).

Filingpro (talk) 19:56, 13 January 2016 (UTC)


 * Adding later-no-harm would open a can of worms. Some election methods (e.g. anti-plurality or Coombs) are defined only for complete individual preferences. For other election methods (e.g. plurality voting or supplementary voting), it is disputed whether they satisfy later-no-harm. Markus Schulze 19:27, 14 January 2016 (UTC)


 * I think better to include known and highly relevant information, rather than exclude such information on account of unrelated and largely irrelevant issues.


 * I propose we add compliances with footnotes, if necessary, to address alternative reasoning.
 * Plurality Later-No-Harm "Not Applicable", Later-No-Help "Not Applicable" - footnote: "Plurality voting allows the voter to choose only one candidate, so it is not possible to help or harm the chosen candidate by voting for secondary candidates. Plurality voting can be considered to pass both Later-No-Help and Later-No-Harm when considering that a voter's unexpressed secondary preferences can not help or harm their chosen candidate."
 * POST CORRECTION: Applying the same manner Anti-Plurality is treated for compliance with Reversal Symmetry in this article, Plurality does PASS both Later-No-Harm and Later-No-Help.Filingpro (talk) 03:01, 5 April 2016 (UTC)
 * Supplementary Vote: Later-No-Harm PASS, Later-No-Help PASS - footnote: "A voter's supplementary vote can not help or harm their preferred candidate."
 * Coombs Later-No-Harm FAIL, Later-No-Help FAIL - footnote: "When a truncated preference listing is considered to apportion last place votes among all unranked candidates, a voter may help or harm their preferred candidates by ranking additional ones."
 * Anti-Plurality Later-No-Harm FAIL, Later-No-Help PASS - footnote: "When a voter having an ordered preference of the candidates is considered to vote for all candidates other than their least preferred, their vote for any later preferred candidate may harm but not help any earlier candidate."
 * POST CORRECTION: My error; Anti-Plurality does FAIL Later-No-Help because the probability of a preferred candidate being elected can increase as later preference are added to the ballot (by increasing the probability of an opponent being listed last).Filingpro (talk) 03:01, 5 April 2016 (UTC)
 * ALTERNATIVE SOLUTION 1: Remove potentially controversial, esoteric and less common methods from table, such as Coombs, Anti-Plurality.
 * ALTERNATIVE SOLUTION 2: Create two tables (1) "Comparison To Other Condorcet Methods" (2) "Comparison To Methods Commonly Used For Government Elections"
 * I believe Schulze is a compelling resolution method and should be considered seriously against other real-world government election systems (e.g. Top-Two Runoff, IRV). In my view, without including Later-No-Harm/Help we make no less than a mockery of the comparison.
 * Filingpro (talk) 05:25, 17 January 2016 (UTC)

A comparison table with your recommended additions already exists at Voting_system (scroll down past the text). That table is heavily peer-reviewed, and contains lots of the kinds of clarifications you suggest. The table on this page is just a subset of that table. VoteFair (talk) 19:40, 22 January 2016 (UTC)
 * (1) The table here is not a mere subset of the table on the main voting article, because it contains many voting methods not included in the main voting article, especially ones cited by Markus Schulze as being problematic for inclusion of Later-No-Harm such as Coombs, Anti-Plurality, Supplemental Vote. I count at least six other methods not in the main article.
 * (2) If the criterion are "just a subset" of the main table, what is our editorial reasoning for which criteria we include? How would the reader know that we are excluding critically important criteria, such as Later-No-Harm and Later-No-Help? Without this disclosure the reader is provided an entirely invalid "comparison of voting systems". Also, if the determinations from the main table are peer-reviewed, then why would they not propagate here? It would seem more logical to include important criteria, rather than include esoteric voting methods not included in the main voting article. Filingpro (talk) 10:14, 19 March 2016 (UTC)

PROPOSED REMEDIES: If the goal is to compare Schulze to more esoteric methods without introducing Later-No-Help/Harm controversy, for the purpose of offering information different than the main article, this goal should not trump comparing Schulze to common real-world methods in a meaningful way. OPTION 1: Keep the existing table and re-title it appropriately. Create a second table "Comparison To Methods Commonly Used For Government Elections". Include Plurality, Top-Two Runoff, IRV (perhaps others). Use criteria that distinguish the methods' performance, e.g. Monotonic, Mutual Majority, Condorcet, Condorcet Loser, Clone Independence, Participation, Later-No-Harm, Later-No-Help, Summability. OPTION 2: Clarify what is excluded from this table and provide a link to the main comparison table. "The following table compares the Schulze method with other preferential single-winner election methods using some but not all known voting criteria. For a complete comparison of Schulze to commonly used election methods, including strategic voting criteria such as Later-No-Harm and Later-No-Help, refer to the voting methods comparison chart. (link) Filingpro (talk) 10:14, 19 March 2016 (UTC)


 * Creating one table for "esoteric methods" and one table with other criteria for "methods commonly used for government elections" would be weaseling. We would apply different standards for different methods. Furthermore, the allegedly omitted criteria are already mentioned in the section "Failed criteria" of the Schulze method article. Markus Schulze 14:38, 19 March 2016 (UTC)
 * (1) The source of weaseling is the existing article "Comparison of voting systems" which implies it is a complete comparison, which it is not. The table is sorted by performance, to emphasize better performing methods, yet criteria are omitted which weasel the results. The double standard is the existing article which introduces criteria on the one hand, but then selectively applies certain criteria and not others.
 * (2) The original remedy I proposed addresses the source of the problem by adding LNH/LNH. On what basis is the determination of "Reversal Symmetry" and "Clone Proof" for Coombs, Anti-Plurality less controversial than of LNHarm/Help? Where is the "peer-reviewed" source for these determinations? Filingpro (talk) 20:13, 19 March 2016 (UTC)

Based on responses here, I believe the best remedy: We put the LNH determinations here as either YES/NO, and see if a controversy exists. I see no evidence given that the LNH/Harm determinations are provided in the main table. Those controversies can be resolved in the main table and propagated here. If methods are not included in the main table for lack of significance or because their determinations are unknown, they should not be included here, forcing the removal of critical and known information, ultimately misrepresenting the relative performance of Schulze and other methods. Filingpro (talk) 20:13, 19 March 2016 (UTC) ALTERNATE REMEDY: STEP 1. Change title to "Partial Comparison of Voting Systems"* STEP 2. Remove any method from the table that is known to pass either Later-No-Help, Later-No-Harm, or Favorite Betrayal. Since Schulze fails all three, the remaining methods in the table would provide an accurate comparison of performance. This would be of usefulness to the reader. Filingpro (talk) 21:00, 19 March 2016 (UTC) *IMPORTANT NOTE: This latter remedy is akin to my earlier solution "Comparison To Other Condorcet Methods". A second table "Comparison to Runoff Systems" or "Comparison To Positional Voting Systems" would not be warranted as that would be better placed in a general article regarding Condorcet or Positional methods, unless Schulze's Condorcet method's performance is particularly unique. Filingpro (talk) 22:07, 19 March 2016 (UTC) Or, what is the goal of the table, as opposed to the main article table? For example, the goal might be to compare Schulze performance with respect to global criteria (i.e. non-strategic), as introduced by Woodall http://www.votingmatters.org.uk/ISSUE3/P5.HTM This would remove Monotonic, Participation, Later-No-Help/Harm etc. The table could be appropriately titled. Filingpro (talk) 23:39, 19 March 2016 (UTC)


 * Dear Filingpro, you ask: "On what basis is the determination of 'Reversal Symmetry' and 'Clone Proof' for Coombs, Anti-Plurality less controversial than of LNHarm/Help?" The presumptions of the reversal symmetry criterion and the independence of clones criterion can be applied to Coombs and anti-plurality. Therefore, it can be checked whether these methods satisfy these criteria. On the other side, the presumptions of later-no-help and later-no-harm cannot be applied to Coombs and anti-plurality, because Coombs and anti-plurality are defined only for complete individual rankings. Therefore, it cannot be checked whether Coombs and anti-plurality satisfy later-no-help or later-no-harm. Markus Schulze 06:58, 20 March 2016 (UTC)
 * Yes I see the distinction however at this point I see this particular question as a red herring, and therefore I retract it (despite my conjecture Later-No-Help/Harm can indeed be logically applied to Coombs and Anti-plurality, under a unified model). Meanwhile the article misrepresents the performance comparison of Schulze against methods that pass Later-No-Help, Later-No-Harm. To make progress on this issue, please respond or concur with remedy above "ALTERNATE REMEDY" and the question ascertaining the very goal of the table itself. In short, we can omit LNHarm/Help which Schulze fail, but we can not also include methods that pass LNHarm/Help in a performance comparison and call it a valid comparison. These methods can be properly compared in the main voting system table. Please let me know if you have any questions. Thank you Filingpro (talk) 08:12, 20 March 2016 (UTC)


 * Dear Filingpro, first of all, there isn't even an article on later-no-help. When you are so obsessed by later-no-help, then the first thing that you should do is to create an article on later-no-help.
 * Second, whether Coombs and anti-plurality satisfy later-no-harm is discussed neither at the Coombs article nor at the anti-plurality article nor at the later-no-harm article. But you want to discuss your "unified model" (that allegedly tells us how later-no-harm could be applied to Coombs and anti-plurality) at great length at the Schulze method article! That's ridiculous! How later-no-harm could be applied to Coombs and anti-plurality should first be discussed at the Coombs article, the anti-plurality article and/or the later-no-harm article. Markus Schulze 09:25, 20 March 2016 (UTC)
 * I believe you almost entirely misread my last statement. I am now simply suggesting that methods for which Later-No-Harm is passed and undisputed, such as IRV, we remove them from your table . If you like, we can treat Later-No-Help separately. Regards Filingpro (talk) 10:54, 20 March 2016 (UTC)
 * Waiting for response 1-2 weeks before removing (see underline above). Please let me know if you would like further clarification. Thanks Filingpro (talk) 04:40, 21 March 2016 (UTC)
 * Dear Filingpro, I will classify your behavior as vandalism. Markus Schulze 06:44, 21 March 2016 (UTC)
 * Dear Markus Schulze, you are an esteemed contributor to the field of social choice, and I am grateful for your contributions: the Schulze method, voting publications, and wiki contributions. I will do my best to be respectful in any editorial deliberation with you, and I apologize if I have been disrespectful here.
 * It seems to me there is a misunderstanding. I will start a new section below clarifying my editorial issue with the article. Kindly Filingpro (talk) 06:09, 24 March 2016 (UTC)

Later-No-Harm/Help Added To Table
Added columns Later-no-harm and Later-no-help without removing methods as per general consensus.

We disclose clearly the assumptions made for compliances of Anti-Plurality, Coombs, and Dodgson, and importantly we make clear the assumptions for non-applicability, so the reader can decide for themselves.

I believe this disclosure addresses any WP:OR problem, while we advance no new theory, only how we normalize the inputs in the table so all methods receive the same input.

By doing so we better distinguish the methods, and the compliances are obviously consistent with observable behavior. For example, Anti-Plurality, Coombs, and Dodgson are vulnerable to burying; their failure of Later-No-Help distinguishes them from compliant methods.

I believe this is better than using ‘NA’ in the table. Filingpro (talk) 20:48, 10 April 2016 (UTC)

RfC: Incomplete Comparison Of Runoff Systems To Schulze In Compliance Table (Requesting Removal)

 * UPDATE: A solution posted to the article - see new section below "Later-No-Harm/Help Added To Table" Filingpro (talk) 20:56, 10 April 2016 (UTC)

It is axiomatic to a compliance table each method added is a direct comparison to each other method.

In deciding which method to use for a three way election, the reader would not be given adequate information in the comparison table to make an informed choice between Schulze and runoff systems (e.g. IRV), because nearly every criteria Schulze satisfies is revealed, but Later-No-Harm and Later-No-Help are omitted, which IRV satisfies and Schulze does not, and which are fundamental to their differentiation.

Since the comparison does not provide for an informed choice, I suggest we remove runoff methods from the table. Schulze is better compared to runoff systems in the main voting article's compliance table.

The counterargument to this proposal I do not find persuasive, that Schulze's failure of LNH is mentioned earlier in the article.
 * Problem 1: Proper treatment of a subject in one area does not justify improper treatment in another.
 * Problem 2: If the criterion is important enough to cite Schulze's failure, it is only more important in the direct comparison to reveal runoff systems pass, or to simply not include them in the table.

I have not yet heard justification for why runoff systems must be included in this comparison table, specifically in the Schulze article, which contains only a subset of the criteria. I believe the reader is well served in this article by seeing a direct comparison between Schulze and other simultaneous election methods, but not against sequential runoff systems whose relative performance is misrepresented here (albeit inadvertently). Filingpro (talk) 06:54, 24 March 2016 (UTC)
 * Schulze is compared against instant-runoff because they solve the same problem, choosing a winner from preference ballots. It would make no sense to have a comparison of such methods and omit one of the main alternatives. If the comparison is missing some important properties then they can be added. —David Eppstein (talk) 15:53, 24 March 2016 (UTC)
 * Thank you David Eppstein for joining and contributions to the field. The remedy you propose was also my starting point (section above "Suggest Adding Later-No-Help and Later No-Harm"). The problem is some editors claim LNHarm is disputed for Coombs, Anti-plurality (see editor Schulze comment below). Editorial priority is currently given to including these methods, and to omit the Later-No-Harm/Help criterion. Can you please advise how we might remedy this problem? In your reply you suggest IRV is a "main alternative" and LNHarm/Help are "important properties" to which I agree. Should we...
 * (A) Remove Anti-Plurality/Coombs due to controversy (and less relevance) and add Later-NoHarm/Help?
 * (B) Keep all methods while adding LNHarm/Help, and if so can you tell us how to complete the compliances?
 * (C) Remove sequential runoff methods from table (or non-condorcet methods), providing the reader an accurate comparison of Schulze to other simultaneous methods (or Condorcet methods), distinguishing the table from the main voting article table, providing added value?
 * (D) Leave the direct performance comparison between Schulze and IRV in the table without including LNHarm/Help?
 * (E) Other?
 * In my view, "D" is not acceptable because any comparison of a simultaneous voting method such as Schulze to a sequential runoff method, without inclusion of Later-No-Harm is a false comparison. Since we would not justify making this false comparison on its own, we can not justify the false comparison merely for external reasons (i.e. disputes re Coombs/Anti-Plurality - not used in elections or not as commonly used).
 * The current article does not to include rating ballot methods (Approval, Range, Majority Judgment etc.), despite they “solve the same problem”. Why then can we not remove sequential runoff methods ( or remove controversial and esoteric methods which can't be evaluated with respect to "important criteria"- added Filingpro (talk) 21:06, 26 March 2016 (UTC)), unless they can be properly compared? Also, what should be the editorial goal of this table, as opposed to the compliance table in the main voting article, where IRV and Schulze are properly compared? Thanks for any recommendations. Filingpro (talk) 19:47, 26 March 2016 (UTC)


 * Adding later-no-harm to the table would open a can of worms, because later-no-harm isn't really a well-defined criterion. This can best be seen by the large number of election methods for which it is disputed whether they satisfy or violate later-no-harm. For some methods, this is disputed because these methods are defined only for complete individual preferences (e.g. Coombs, anti-plurality). For some methods, this is disputed because these methods don't allow voters to cast more than a limited number of preferences (e.g. plurality voting, supplementary voting). For some methods, this is disputed because there are different ways how these methods could be generalized to situations with incomplete individual preferences; for example, the Minimax Condorcet article says: "When the pairwise opposition variant is used, Minimax also does not satisfy the Condorcet criterion. However, when equal-ranking is permitted, there is never an incentive to put one's first-choice candidate below another one on one's ranking. It also satisfies the Later-no-harm criterion, which means that by listing additional, lower preferences in one's ranking, one cannot cause a preferred candidate to lose." However, removing instant-runoff voting from the table is not an appropriate answer to the problems of later-no-harm, because then everybody could propose a lousily defined criterion for his favorite election method and then demand a special treatment for his favorite method. Markus Schulze 19:45, 24 March 2016 (UTC)


 * Comment. I can understand the article, but I cannot understand this RfC. What is a "compliance table"? What is a "runoff method"? These phrases do not occur in the article. And what is "the table" in the underlined proposal? Maproom (talk) 07:56, 26 March 2016 (UTC)


 * With "compliance table" or "the table", Filingpro means this table. With "runoff method", Filingpro means instant-runoff voting. Basically, this RfC says that instant-runoff voting should be removed from this table because instant-runoff voting satisfies later-no-harm while it is not possible to say which of the other methods satisfies later-no-harm. Markus Schulze 10:35, 26 March 2016 (UTC)
 * To my mind that is a really bad reason for removing it from the table. —David Eppstein (talk) 20:15, 26 March 2016 (UTC)
 * Could you reply to my response above and offer argumentation for "bad" if still applicable, because while I agree with much of editor Schulze wrote above, I don't agree entirely with the statement of my "reason" which you seem to be responding to. Would it be fair to ask you to comment on my statement of the problem (above - see A, B, C, D, E) rather than Schulze since I am raising the issue? I don't agree with the statement of my reason as provided here (while I do not suggest Schulze intending to misrepresent but only to clarify) Kindly Filingpro (talk) 21:22, 26 March 2016 (UTC)
 * To David Eppstein, put another way, you said Later-No-Help/Harm are "important criteria" and should be added. Do you suggest remedy (A) or (B) in my response further above? Thanks for any help you can provide. Filingpro (talk) 22:44, 26 March 2016 (UTC)
 * I did not say that LNH is important. What I said was that, if the table is missing important criteria, then the correct fix is to add columns, not to delete rows. —David Eppstein (talk) 23:21, 26 March 2016 (UTC)
 * Thank you for clarification. Apologies for misrepresentation. I believe we must address the concerns of editor Schulze before adding columns. Based on your helpful feedback I have a new proposal below. Filingpro (talk) 01:46, 27 March 2016 (UTC)

NEW PROPOSAL:
I believe the following proposal builds upon the feedback from all editors, and improves the article. ARGUMENTATION: We do not include voting systems having different ballot types than Schulze (Approval, Majority Judgment) because they are not subject to the same criteria. We must be be consistent. Schulze method operates on truncated preference ballots. Coombs and Anti-Plurality do not. These require different input. I believe this to be the central problem. ACTION: (1) I will add an article for Later-No-Help (2) We update the Schulze article table adding LNHarm and LNHelp and include voting systems that accept the same input as Schulze - i.e. truncated preference listings, so that we make a fair and complete comparison of methods of the same type. (Note: Plurality and various Two-Round Runoff systems operate on truncated preference input) Filingpro (talk) 01:46, 27 March 2016 (UTC)


 * Dear Filingpro, and what do you do about the fact that it is disputed for many election methods whether they satisfy or violate later-no-harm or later-no-help? Markus Schulze 08:20, 27 March 2016 (UTC)
 * As this article is specifically on the Schulze method, and because Schulze accepts as input a truncated preference listing, I propose we include all methods in the table that can operate unambiguously on a truncated preference listing, so that we make a fair and complete comparison of methods of the same type as Schulze. Do you agree that any method that can unambiguously receive as input a truncated preference listing also has knowable determinations for Later-No-Help and Later-No-Harm? To be clear, this would mean that Anti-Plurality is not included in the table just as we do not include Range Voting etc., because neither accepts as input truncated preference listings, as Schulze does. My opinion is that by making complete and legitimate performance comparison of Schulze to every known truncated preference method, while including Later-No-Harm and Later-No-Help criterion (which are defined precisely for truncated preference methods like Schulze), then the accuracy and credibility of a Schulze performance comparison is enhanced. This would give the reader a very clear view of how these truncated methods actually compare to each other in performance. It is my view, that comparing Schulze to other methods of the same type but excluding important criteria (whose compliance is in fact unambiguous), damages the comparison and damages the legitimacy of the table. In my opinion it would be a mistake for us to force inclusion of other methods that require different ballot types as input (e.g. Coombs), to justify removing important criteria, thereby delegitimizing the comparison of methods that do have the same type, particularly methods deemed as "main" methods. I believe we are likely in agreement about voting theory, while this is an editorial issue. Thank you for your question and engaging in the discussion. I am hoping you will see this as an optimal solution to both of our concerns that presents Schulze method in the most accurate and complete way possible. I would begin by creating an article for Later-No-Help as you suggested before making any edits. Regards Filingpro (talk) 11:36, 27 March 2016 (UTC)


 * Dear Filingpro, your proposals are not acceptable. You are weaseling to get somehow some special treatment for instant-runoff voting. Markus Schulze 16:31, 27 March 2016 (UTC)
 * I will add Later-No-Help article and then propose a new RfC for editors to comment on two possible tables. My goal is to improve the Schulze article, by providing a more accurate performance comparison of Schulze to methods of the same type, by including applicable criteria that are fundamental to a reader making an informed choice. Respectfully Filingpro (talk) 18:38, 27 March 2016 (UTC)
 * If you like, you can clarify your position now for the upcoming RfC, so that when I post the RfC your position is correctly represented, below...
 * Upcoming RfC question to editors: Should we:
 * (A) Include Later-No-Harm/Help and exclude Coombs/Anti-plurality, or
 * (B) Include Coombs/Anti-plurality and exclude Later-No-Harm/Help?
 * My argument for A is the reader is better served by making a more complete comparison of Schulze to every known method of the same type - i.e. that receive as input a truncated preference listing, rather than include Coombs/Anti-Plurality which require different input and therefore not subject to the same criteria.
 * Your argument for B is the reader is better served by comparing Schulze to Coombs/Anti-pluralty to include more methods, rather than include Later-No-Harm/Help, which is not knowable for these methods. Including Later-No-Harm/Help over inclusion of Coombs/Anti-Plurality is weaseling to promote methods that pass these criteria.
 * Is that an accurate summary of your argumentation? Thanks for any clarification. Regards Filingpro (talk) 18:38, 27 March 2016 (UTC)


 * Dear Filingpro, if I understand you correctly, then proposal (B) implies that instant-runoff voting should be removed from the table. Both proposals, (A) and (B), are not acceptable. Again, I will consider your edits as vandalism. Markus Schulze 20:33, 27 March 2016 (UTC)
 * Proposal (B) includes IRV (same table as now). Filingpro (talk) 15:36, 28 March 2016 (UTC)

QUESTION 1 for Markus Schulze re: Anti-Plurality failure of Reversal Symmetry. You say "presumptions of the reversal symmetry criterion...can be applied to ...anti-plurality." Reversal symmetry presumes a voter preference ballot. To apply these presumptions to a "Vote Against" ballot which only records the voter's most opposed candidate, we are not using a literal "Vote Against" ballot, instead we are assuming the voter is required to submit a complete preference listing (e.g. abc by writing them sequentially as Woodall suggests). Is that correct? Filingpro (talk) 15:36, 28 March 2016 (UTC) QUESTION 2 for Markus Schulze - What is our editorial standard for determining compliances, with respect to hypothetical challenges of WP:OR? For example, there is no mention of the failure of Anti-Plurality to satisfy Reversal Symmetry in either article on Wikipedia, nor is there a citation in Schulze article. Is that correct? If so, then is the standard whether we can logically apply the voting method to the presumptions of the criteria (e.g. taking liberty to change the ballot to match the presumptions), and if the results are mathematically computable? Is that correct? Filingpro (talk) 15:36, 28 March 2016 (UTC)


 * Dear Filingpro, here is the difference: On the one side, it is possible to check whether Coombs and anti-plurality satisfy or violate reversal symmetry simply by looking at the definitions and without having to make additional presumptions. On the other side, it is not possible to check whether Coombs and anti-plurality satisfy or violate later-no-harm simply by looking at the definitions and without having to make additional presumptions. You claim that you have a "unified model" (that allegedly tells us how later-no-harm could be applied to Coombs and anti-plurality). But your "unified model" is original research, at best. Markus Schulze 16:10, 28 March 2016 (UTC)
 * (1) I never suggested proposing a "unified model" in Wikipedia (you will see this was a parenthetical remark - i.e. merely a conjecture that one exists)
 * (2) In QUESTION 1, I am asking specifically how we arrive at Anti-Plurality failure of Reversal Symmetry in the Schulze article. Can you please answer? Filingpro (talk) 02:04, 29 March 2016 (UTC)


 * It seems to me having a table that compares the subject of the article to some instant-runoff voting methods but not all could be misleading. It might leave a false impression about the primacy on utilitarian criteria of a particular method.  If I'm understanding the subject matter correctly LNH can be determined for some methods.  Therefore, it seems you'd add the column note those methods where it can be determined with the appropriate notation and for those where it cannot be determined have that as a notation. Klaun (talk) 23:55, 28 March 2016 (UTC)
 * Generally agreed.
 * Clarification: My "UPDATED PROPOSAL" above includes all runoff methods, and every known voting method capable of receiving the same input as Schulze, so all criteria that apply to one apply to all, making an accurate comparison. The problem occurs when we start introducing methods that require different input, and then controversies arise as to how criteria are applied. You will notice, for example, no editor is demanding to add voting systems to this table that receive as input scoring, rating, and approvals, because their behaviour with respect to the criteria can be less clear, and dilutes the focus of the article. What I object to, is that we have added two rather obscure (i.e. unused) methods to the table that have different input requirements than Schulze, and consequently we exclude criteria which are fundamental to comparing Schulze to other main methods (and also shows Schulze more favorably - in fact Schulze is a near perfect voting method, buts its primary weakness is its failure of the criteria that are excluded from its comparison).
 * Your suggestion of distinguishing compliances that can not be determined and making notations is I think worth considering (also my initial inclination when I first proposed adding LNH) although raises editorial questions as to where we source these determinations etc. and whether they are better resolved first in the main voting article compliance table or in the articles for the various methods and criteria. Thanks for any suggestions. Filingpro (talk) 03:10, 29 March 2016 (UTC)

Comment: Original rationale seems very odd and weak to me. The current article places no WP:UNDUE weight on the strengths of the method, nor does it avoid all criticism. LN(harm/help) are very interesting of course, but their lack of current inclusion is not some unfair bolstering of Schulze method. Revised proposal (which I put in new section) seems much better, and I do like the idea to only include methods that use the same input. IRV in this sense is comparable to Schulze method. I advise OP and others to be wary of moving the goalposts re: this current RfC. Participation by Mr. Schulze here is is interesting. While his expertise is appreciated I will also remind myself that he is clearly highly WP:INVOLVED. While I believe him that it is contested whether certain methods comply with LNH, I'm not sure that I understand his comment that it "isn't really a well-defined criterion". I understand that (non)compliance is hard to rigorously prove, but our article at least makes the definition of the criterion seem clear, simple, and uncontested. This may or may not matter much for the current discussion. At present I don't see the problem with including a LNH column in the table. The fact that many methods would have a blank or N/A under LN(harm/help) due to lack of RS is also not a big problem in my opinion. SemanticMantis (talk) 14:02, 4 April 2016 (UTC)
 * Generally agreed regarding remedies. This was my very first proposal "Add L-N-Harm/Help" long before RfC by Schulze. Consensus seems to be building around adding columns. Filingpro (talk) 23:00, 5 April 2016 (UTC)
 * Let's say that there are five candidates (A,B,C,D,E). Let's say that the sincere opinion of a voter is A>B>C>D>E. That means that this voter prefers A to B to C to D to E. Now, what does it mean when we say that this voter casts one preference or two preferences?
 * Supporters of instant-runoff voting usually presume that voters have strong preferences on who is the best candidate, but that the voters are rather indifferent on who is the worst candidate. Therefore, a supporter of instant-runoff voting will argue that a voter who casts only one preference is a voter who votes A>B=C=D=E and a voter who casts two preferences is a voter who votes A>B>C=D=E.
 * Supporters of Coombs usually presume that voters have strong preferences on who is the worst candidate, but that the voters are rather indifferent on who is the best candidate. Therefore, a supporter of Coombs will argue that a voter who casts only one preference is a voter who votes A=B=C=D>E and a voter who casts two preferences is a voter who votes A=B=C>D>E.
 * Both, the instant-runoff supporters and the Coombs supporters, claim that only their method has the property that casting a weaker preference can never hurt or help a stronger preference. The whole argumentation is arbitrary. The difference between these two methods is not that the one has this property and the other doesn't. They only differ in which preferences they believe to be stronger. Markus Schulze 18:21, 5 April 2016 (UTC)
 * I see how Coombs or any method could use a reverse order ballot, but that would mean Coombs fails Woodall's Majority, which it does not. Our table applies input with same polarity to each method so results have meaning. For example, for Anti-Plurality we assume rankings are in preferred order. Filingpro (talk) 22:43, 5 April 2016 (UTC)
 * What does "polarity" mean in this context? Markus Schulze 04:33, 6 April 2016 (UTC)
 * In Woodall's framework, the listing abc denotes the voter places a first, b second, c third etc. On a reverse order ballot, without normalizing the input, ' a ' in Woodall's listing would be least preferred by the voter rather than first preferred (i.e. opposite meaning). The polarity means the direction of the voter's ordinal preferences in the listing. If we reverse the polarity, Schulze fails Woodall's Majority and Condorcet, which it does not. Filingpro (talk) 21:35, 6 April 2016 (UTC)
 * Dear Filingpro, the question is not whether the individual voter ranks the candidates from most preferred to least preferred or from least preferred to most preferred. The question is whether the individual voter has strong preferences between his most preferred candidates or strong preferences between his least preferred candidates. Supporters of instant-runoff voting presume that the individual voter has strong preferences between his most preferred candidates and weak preferences between his least preferred candidates.
 * (Re: Coombs) I believe you suggest Woodall's “later preference” for Coombs means more preferred by the voter, rather than less preferred? The problem I see is then Coombs fails Woodall's Majority. Do you see the problem? Filingpro (talk) 20:04, 7 April 2016 (UTC)
 * Your claims about the Schulze method are incorrect. The Schulze method only presumes that the individual voter casts a strict weak order. Furthermore, the Schulze method satisfies reversal symmetry. Therefore, reversing the "polarity" has no impact on the result of the elections. Markus Schulze 04:58, 7 April 2016 (UTC)
 * I said if the voter's least preferred choice is first (instead of last ) in Woodall's preference listing, then Schulze fails Woodall's Majority and Condorcet, which leads to a contradiction. Does that make sense? If the Schulze analogy is confusing, I suggest we discuss Coombs (please see comment above). Filingpro (talk) 20:04, 7 April 2016 (UTC)
 * Dear Filingpro, even when the voters rank the candidates from most preferred to least preferred, a voter can have a strong opinion on who is the worst candidate and be rather indifferent on who is the best candidate. For example: A voter could say that Trump shouldn't be elected; at the same time, this voter could have no strong opinion on whether Cruz or Kasich should win. Does that make sense to you? Markus Schulze 04:17, 8 April 2016 (UTC)
 * Of course but what is the point you want to make about LNH? What I'm saying is for the voter you describe, Woodall's "later preference" means Trump is later than Cruz & Kasich in Woodall's preference listing. Just as in Anti-Plurality, we consider the compliance by assuming a complete listing whereby the candidate at the end of the listing is voted against. Filingpro (talk) 07:08, 9 April 2016 (UTC)
 * Oh, wow, that's perverse. Thanks Markus, I get it now. I thought we just didn't allow votes like A>B=C=D=E. The vote should either be full, e.g. A>B...>E or it gets truncated to e.g. A>B if the form is not completed. Anyway, I don't think this in and of itself is a strong reason to not have LNH in the table. Maybe you could put sufficient warnings and critiques in the LNH articles to better illustrate their potential problems and potential for ill definition. 14:36, 6 April 2016 (UTC)
 * Agreed. Filingpro (talk) 20:04, 7 April 2016 (UTC)

UPDATE: A solution posted to the article - see new section below "Later-No-Harm/Help Added To Table" Filingpro (talk) 20:56, 10 April 2016 (UTC)

Ordering Columns In Compliance Table
I suggest we list criteria first by winner selection, then strategic voting, then strategic nomination, then counting:

Majority Majority Loser Mutual Majority Condorcet Condorcet Loser Smith Reversal Symmetry Participation, Consistency Monotonicity Later-no-harm Later-no-help Clone Independence ISDA LIIA Polynomial Time Resolvability

We sort by number of compliances, and secondary sort by compliances left to right. We can put Schulze at top as long as table correctly titled. Filingpro (talk) 21:05, 10 April 2016 (UTC)

Cool python implementation
https://github.com/bjornlevi/schulze — Preceding unsigned comment added by 89.17.137.38 (talk) 19:05, 5 June 2016 (UTC)

Complete garbage
Sorry Schulze, you're completely obtuseness to include the "Tennessee example" and stubbornly stick with this obscure spiderweb map makes this method all but incomprehensible to all but the greatest autists. Sad really, as this would be an excellent method to elect single winner executive positions over IRV. And you wonder why the two round system/IRV/STV are used the world over infinitely more than your still confusing method. — Preceding unsigned comment added by 64.66.22.220 (talk) 19:09, 12 May 2016 (UTC)


 * As Albert Einstein said: "Make things as simple as possible, but not simpler." Markus Schulze 09:04, 13 May 2016 (UTC)

But the section beginning "An alternative, slower, way to describe the winner of the Schulze method" is vastly clearer to ordinary people - even people with, say, a PhD in physics. Sure, if you happen to already know graph theory then the system described above may be briefer. Most people do not know graph theory. The iterative process described is something anyone can follow. If it is correct (and as far as I can tell, it is), then it should be presented first.

To put it another way, it's like writing a tiny command-line utility in c, and #include-ing the whole gnu toolkit because using the data structures makes the elegance of the algorithm clearer and makes the program 1 line shorter... except, in this case, instead of including something easily acquired in a short time like the gnu toolkit, it takes a graduate-level course in math. -- Luke A Somers 2016-09-18 — Preceding unsigned comment added by 100.14.175.181 (talk) 15:07, 18 September 2016 (UTC)

MinMax set and prudence criteria
Stubs for these 2 criteria would be nice too. --Wat 20

I tried to add a Column for MinMax to the table, but changing the template is not changing it on the Schulze Method page. Not sure why. Schulze Method passes MinMax criterion but Ranked Pairs (Tideman) does not, and this table should include that information to help differentiate the two. --Owen — Preceding unsigned comment added by 71.201.20.135 (talk) 17:55, 28 May 2016 (UTC)

I am open to "MiniMax criterion". Is there a citation or reference to this criterion? I would like to understand better. My understanding of the MiniMax article is that the Minimax decision for a given player is the choice that will give the least worst outcome given the range of choices by the other players in a game; hence uncertainty is intrinsic to the principle, but I see a contradiction with regard to application to a preference aggregation algorithm where the voters preferences are certain. Meanwhile, my understanding with regard to preference aggregation algorithms, MiniMax is a heuristic that chooses the alternative with the least-worst pairwise defeat against other alternatives. However, I believe that Schulze returns different output than MiniMax voting methods, correct? If so, I am wondering how Schulze can satisfy "MiniMax"? Thanks for any clarification. Filingpro (talk) 18:23, 22 July 2016 (UTC)

NOTE: PROPOSAL TO REMOVE MINIMAX CRITERION

Summary of reasoning: Schulze returns different output than Minimax methods, while the MiniMax decision of a given player is different than a criterion for a voting system.

Will wait 3 weeks before removal. Filingpro (talk) 07:45, 27 August 2016 (UTC)

Will not have time to return to do the removal for several months, if someone else would like to do so. Filingpro (talk) 03:27, 22 November 2016 (UTC)

Made change on template but not updating on Schulze method page. This needs to be fixed.Filingpro (talk) 18:43, 26 November 2016 (UTC)

A similar method called "Schulze" in an article
In this article on Medium, they use the term "Schulze" for a similar but much simpler method. They actually use the exact same example as here (starting at the third graph from the top, "Ok so here's another election..."), but they eliminate the weakest edge in the graph (E→A with strength 23), disregarding the longer but stronger path (E→D→C→B→A with strength 25). This produces a different winner. I assume they have just misunderstood what the Schulze method is, but the simplicity is alluring, so I just wanted to ask if the drawbacks of this simpler method have been assessed. 94.255.173.199 (talk) 11:01, 29 September 2018 (UTC)


 * In the Wikipedia article, the arrows always go from the winner to the loser of the respective pairwise contest. However, in the Medium article, the arrows always go from the loser to the winner of the respective pairwise contest. Therefore, the example in the Medium article is not the exact same example as here, it is the exact inversion of the example in the Wikipedia article. Markus Schulze 14:38, 1 October 2018 (UTC)

Something that I don't understand
The article says: "To avoid cluttering the diagram, an arrow has only been drawn from X to Y when d[X, Y] > d[Y, X] (i.e. the table cells with light green background), omitting the one in the opposite direction (the table cells with light red background)."

Why is it a legal move to ignore the opposite paths? I mean, I belive it, the article just doesn't explain it. — Preceding unsigned comment added by MainframeXYZ (talk • contribs) 19:28, 12 January 2019 (UTC)


 * Every pairwise win or tie (XY with d[X,Y] &ge; d[Y,X]) is stronger than every pairwise defeat (ZW with d[Z,W] < d[W,Z]).
 * For every pair of candidates AB, there is a path from A to B or a path from B to A that contains no pairwise defeat. This follows directly from the fact that already the link AB is a path from A to B that contains no pairwise defeat or the link BA is a path from B to A that contains no pairwise defeat.
 * Because of these considerations, the strength of a pairwise defeat cannot have an impact on the result of the election. Therefore, links that are pairwise defeats can be ignored. Markus Schulze 10:51, 13 January 2019 (UTC)

Schwartz-minimax explanation
I might be missing something, but it seems like the alternative implementations section could be summed up as applying minimax to the Schwartz set. Isn't this a much simpler way of explaining it? Thirsch7 (talk) 21:25, 11 February 2019 (UTC)


 * No, the Schulze method is not Schwartz-MinMax and the alternative implementation section doesn't claim this. Markus Schulze 10:18, 13 February 2019 (UTC)


 * I understand that this isn't what the alternative implementation section claims, but it seems equivalent to it. If you start with the Schwartz set and continuously remove the smallest defeats until one candidate's row is clear, the first candidate to have a clear row will be the one whose largest defeat is the smallest (the minimax winner). The fact that the Schwartz set is recalculated after each drop is irrelevant because only defeats are removed, and no candidate can be excluded from the Schwartz set after one of their defeats is removed. Maybe this alternative implementation is inaccurate or missing a step in the explanation? Thirsch7 (talk) 00:57, 14 February 2019 (UTC)


 * "The fact that the Schwartz set is recalculated after each drop is irrelevant because only defeats are removed, and no candidate can be excluded from the Schwartz set after one of their defeats is removed." Example: Suppose there are three alternatives A, B, C. Suppose there is a circular tie A > B > C > A. Then the Schwartz set is {A,B,C}. Suppose C > A is the weakest link. Then, when the link C > A is replaced by a pairwise tie C = A, the new Schwartz set is {A}. Markus Schulze 11:24, 17 February 2019 (UTC)


 * But that's just a different way of explaining minimax. A is the winner in that scenario because its largest defeat was the smallest. What I was saying is not that the Schulze set will never shrink, but that it will shrink to leave only the minimax winner. Thirsch7 (talk) 20:14, 17 February 2019 (UTC)


 * See this example. The Schulze winner is C. The Schwartz-MinMax winner is A. Markus Schulze 07:31, 18 February 2019 (UTC)


 * Thanks for that example, but I still think the alternative implementation might not be clear enough. What threw me off about this, I think, is that only the smallest pairwise defeat is eliminated, so it was not clear to me that, in the example you just cited, A would be eliminated from the Schwartz set under this alternative implementation. I think it might be clearer if in that section, both the smallest pairwise defeat and the corresponding pairwise victory were "grayed out." Thanks for the explanations! — Preceding unsigned comment added by Thirsch7 (talk • contribs) 19:54, 22 February 2019 (UTC)


 * I had added that example in 2009 (diff). However, that example was removed by Daveagp in 2011 (diff). I didn't reinsert that example because I didn't want to be accused of starting an edit war. Markus Schulze 09:17, 23 February 2019 (UTC)

Confusion in Implementation
In the implementation section, we have this:

However, in the pseudocode, the end result is:

Should the `Output` line be changed to read the following?


 * i, j, and k are control variables. It makes no difference whether you say that "p[i,j] is the strength of the strongest path from candidate i to candidate j" or "p[j,k] is the strength of the strongest path from candidate j to candidate k". Markus Schulze 08:36, 6 March 2019 (UTC)