Talk:Schulze method/Archive 2

Archive 1

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:

1. d[C,D] > d[D,C] and d[E,F] ≤ d[F,E].
2. d[C,D] ≥ d[D,C] and d[E,F] < d[F,E].
3. d[C,D] > d[D,C] and d[E,F] > d[F,E] and d[C,D] > 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

1. For i = 1,...,(n-1): d[C(i),C(i+1)] > 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:

1. C(1) is identical to X.
2. C(n) is identical to Y.
3. For i = 1,...,(n-1): d[C(i),C(i+1)] > d[C(i+1),C(i)].
4. For i = 1,...,(n-1): d[C(i),C(i+1)] ≥ 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

The matrix of pairwise defeats looks as follows:

	d[*,A]	d[*,B]	d[*,C]	d[*,D]	d[*,E]
d[A,*]		4	5	6	5
d[B,*]	6		4	5	5
d[C,*]	5	6		4	5
d[D,*]	4	5	6		5
d[E,*]	5	5	5	5

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 [1].

(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

The matrix of pairwise defeats looks as follows:

	d[*,A]	d[*,B]	d[*,D]
d[A,*]		5	3
d[B,*]	4		5
d[D,*]	6	4

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:

• 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

Thank you. -- Jokes Free4Me (talk) 21:55, 30 December 2007 (UTC)

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

1. Schwartz criterion → Smith criterion → mutual majority criterion → majority criterion → non-imposition

but the limitation of the format in not allowing multiple inheritance was unfortunate. Perhaps a sub-list?

1. Schwartz criterion
   1. Smith criterion
   2. Mutual majority criterion
   3. Condorcet criterion
   4. Condorcet loser
   5. Majority criterion
   6. Non-dictatorship
   7. Non-imposition
2. 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: [2]. 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:

1. 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 [3].
2. 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 [4].

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 {{show}} template? --Explodicle (T/C) 16:52, 9 July 2008 (UTC)

• In my opinion, the {{show}} 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 {{fact}} tag, and added a {{citations}} 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:

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..

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)

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 [5]. (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:

• 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

Daveagp (talk) 17:35, 24 April 2011 (UTC)

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:

Norman Petry's calculations

A	B	C	D	E	F
4	81.12%	13.09%	5.34%	0.11%	0.34%
5	74.42%	18.03%	6.61%	0.59%	0.35%
6	67.78%	23.48%	7.49%	0.95%	0.30%
7	62.81%	27.92%	7.44%	1.37%	0.46%
8	59.10%	31.58%	7.29%	1.62%	0.41%
9	54.92%	35.13%	7.20%	2.33%	0.42%
10	52.72%	38.31%	5.91%	2.60%	0.46%
11	49.14%	41.95%	5.75%	2.58%	0.58%
12	47.75%	43.82%	5.26%	2.68%	0.49%
13	44.82%	46.78%	4.85%	2.97%	0.58%
14	42.54%	48.94%	4.34%	3.57%	0.61%
15	41.22%	50.46%	4.25%	3.45%	0.62%

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)