Talk:Schulze method/Archive 1

Untitled
Sorry! But I don't think the article made 100% clear the fact on what kind of a voting ballot voters are given. Are they supposed to rank in numerical order their preferences? --Tmh 12:53, 13 Sep 2004 (UTC)

I added the following sentence in the procedure section: "The voters cast their ballots by ranking the candidates according to their preferences, just like for any othe Condorcet election." AugustinMa 00:06, 18 Sep 2004 (UTC)

Criteria
A table in Voting_system says CSSD complies with the Strategy-Free criterion, does not comply with the Participation criterion, and it is unknown whether it complies with the Favorite Betrayal criterion. Meanwhile Participation criterion says "Any voting system that does not satisfy the Participation criterion could not satisfy either the Favorite Betrayal criterion (FBC) or the Strategy-Free criterion (SFC)." Some mistake here I think. --Henrygb 18:21, 13 Nov 2004 (UTC)

Yes, there is definitely some mistake. Very specifically:

The Participation criterion article says "Condorcet methods . . . fail [the Participation Criterion]," and "Any voting system that does not satisfy the Participation criterion could not satisfy either the Favorite Betrayal criterion (FBC) or the Strategy-Free criterion (SFC)."

If so, then Condorcet methods do not satisfy FBC nor SFC

This article (Cloneproof Schwartz Sequential Dropping) says ". . . CSSD is (by definition) a Condorcet method."

CSSD therefore does not satisfy FBC nor SFC.

This article contradicts this where it says "CSSD satisfies the following criteria: . . . Strategy-Free criterion".

The Strategy-Free criterion article similarly says "Cloneproof Schwartz Sequential Dropping complies with the Strategy-Free Criterion . . . ."

And the Favorite Betrayal criterion article states that "[i]t is not known whether Cloneproof Schwartz Sequential Dropping complies [with the Favorite Betrayal Criterion]."

In the election-methods-list, I see references to a couple of papers that might help resolve these contradictions:


 * Herve Moulin, "Condorcet's Principle Implies the No Show Paradox," Journal of Economic Theory, vol. 45, p. 53-64, 1988.
 * Peter C. Fishburn, Steven J. Brams, "Paradoxes of Preferential Voting," Mathematics Magazine, vol. 56, p. 207-214, 1983.

The first of these is said to demonstrate that Condorcet methods do not satisfy the Participation criterion, as stated in that article. If this and the other quote from that article is true, it must be the Cloneproof Schwartz Sequential Dropping, Strategy-Free criterion, and Favorite Betrayal criterion articles and the table cited by Henrygb that are in error.


 * -- Anon., 19:46, 17 Nov 2004 (UTC)

It has been proven by Hervé Moulin that the Participation criterion and the Condorcet criterion are incompatible. You can find a very short version of this proof here. Therefore, Cloneproof Schwartz Sequential Dropping necessarily violates the Participation criterion.

However, it is trivial to prove that CSSD satisfies the Strategy-Free criterion. Suppose V is the number of voters. Suppose d[X,Y] is the number of voters who strictly prefer candidate X to candidate Y. Then SFC simply says that when d[A,B] > V/2 and d[C,A] < V/2 for every other candidate C, then candidate B must not be elected.

To the best of my knowledge, it has neither been proven that CSSD satisfies the Favorite Betrayal criterion nor that it violates this criterion. -- Markus Schulze 18 Nov 2004


 * My guess is that Strategy-Free criterion is not uniquely defined. In that article it gives a definition "If a Condorcet candidate exists, and if a majority prefers this candidate to another candidate, then the other candidate should not win if that majority votes sincerely and no other voter falsifies any preferences." which looks very weak and biased to Condorcet methods. I would have thought something much stronger was implied by the title.  --Henrygb 17:18, 18 Nov 2004 (UTC)
 * Now I am worried. Some anonymous person has changed the participation criterion article without comment, no doubt as a response to the comments here.  I am starting to feel that this series of articles is becoming an attempt to push a particular POV on voting systems. --Henrygb 17:54, 18 Nov 2004 (UTC)

This is how I interpret Mike Ossipoff's criteria:

Strategy-Free criterion:
 * Suppose (1) d[A,B] > V/2 and (2) the partial individual rankings can be completed in such a manner that candidate A is a Condorcet candidate. Then candidate B must be elected with zero probability.

Generalized Strategy-Free criterion:
 * Suppose (1) d[A,B] > V/2 and (2) the partial individual rankings can be completed in such a manner that candidate A is in the Smith set and candidate B is not in the Smith set. Then candidate B must be elected with zero probability.

Strong Defensive Strategy criterion:
 * Suppose more than V/2 voters strictly prefer candidate A to candidate B and rank candidate B no higher than tied for bottom. Then candidate B must be elected with zero probability.

It is trivial to prove that CSSD satisfies these criteria. -- Markus Schulze 19 Nov 2004

cloneproof
The "cloneproof" part of the name isn't explained in the article. Anyone care to elaborate? --fvw* 20:21, 2004 Nov 18 (UTC)
 * right, the strategic nomination link explains. Thanks. --fvw* 22:47, 2004 Nov 18 (UTC)

Free State Project
To the best of my knowledge, the Free State Project does not use CSSD but the MinMax method. See here. -- Markus Schulze 27 Dec 2004

FBC
I added that CSSD fails FBC. I'll revert it if someone takes issue with this scenario. [mailto:stepjak@yahoo.fr Kevin Venzke]

I want to add: I'm aware that Markus takes issue with Mike Ossipoff's criteria, but as long as CSSD is listed as satisfying certain of those criteria, I can't see why to not list those of Mike's criteria which may be failed. -KV

move from CSSD
I agree with the move from CSSD to Schulze method. CSSD is a very clumsy name. My own preferred name for the method is "beatpath", but Markus was indeed the first to propose the method, and indeed he does prefer "Schulze method". By the way, I'm curious who moved the page. Did you forget to log in, 70.28.246.48? Hermitage 04:12, 19 May 2005 (UTC)

Next time, when you move an article you should log in. Otherwise, the "talk" page, the "history", the "redirect pages", and the "watchlists" are destroyed. MarkusSchulze 12:29, 19 May 2005 (UTC)

some criteria only satisfied by Schulze(wv)...
Some of the criteria listed as "satisfied" are satisfied by Schulze(winning votes), but not by Schulze(margins). For example: Woodall's plurality criterion, SFC, GSFC, and offhand I think minimal defense, SDSC, and WDSC as well. So, someone should make this clear in the article, or remove these criteria from the article. Hermitage 23:36, 20 Jun 2005 (UTC)


 * Actually, neither this article nor the RP article seem to use margins. I'm happy with this situation. KVenzke 03:54, Jun 21, 2005 (UTC)


 * What do you mean when you say that neither article uses margins? If WV is used as the defeat strength definition for the purposes of the satisfied criteria section, I think that this needs to be explicitly stated. If it is not stated, there is no reason to assume that margins will not be used, in which case the satisfied criteria section is not accurate. Hermitage 07:49, 21 Jun 2005 (UTC)


 * Currently, there are 17 criteria in the list of satisfied criteria. As there is at least one variant of the Schulze method that satisfies all 17 criteria simultaneously, I don't see any problem with the fact that not all variants satisfy all 17 criteria.


 * By the way, all links to the "Maximize Affirmed Majorities" article and to the "Maximum Majority Voting" article have been removed from the "Ranked Pairs" article, because Rspeer and Fahrenheit451 considered these articles to be "irrelevant", "original research", and "not well-established enough". If discussing different definitions for the strength of a pairwise defeat in connection with Ranked Pairs is "original research", then this is also "original research" in connection with the Schulze method. Markus Schulze 21 Jun 2005


 * Neither article uses margins because the section explaining cycles uses WV. KVenzke 20:02, Jun 21, 2005 (UTC)


 * I'm not sure which section you mean. At present, the Condorcet method article mentions both margins and WV in a footnote, while citing a page on electionmethods.org (which no longer exists, I believe) as the main argument in favor of WV.
 * If you disagree with F451's deletion of the MMV and MAM links on the RP article, please revert it. I would have done so myself, but I felt that I had already reverted too many of his edits in too short a timespan. I don't think that RSpeer really supported the deletion either, but that he, like me, did not feel strongly enough to revert it.
 * My opinion is that a single page should be created that defines both WV and margins. I suggest "pairwise defeat strength" as the title. I'll mention this on the inluded methods and criteria talk page. --Hermitage 23:22, 21 Jun 2005 (UTC)


 * RSpeer deleted the MAM link on the RP article here and here. Fahrenheit451 deleted this link here and here. It isn't quite clear why RSpeer and Fahrenheit451 have such a strong feeling against this MAM link. But I predict that also the links to your "pairwise defeat strength" article will be deleted because of "original research". Markus Schulze 22 Jun 2005

CDTT
Markus, do you have an example on-hand showing that RP doesn't always elect from the CDTT? KVenzke 03:54, Jun 21, 2005 (UTC)


 * Here is an example where Ranked Pairs chooses from outside the CDTT set.


 * 26 CABD.
 * 20 BDAC.
 * 18 ADCB.
 * 14 CBAD.
 * 08 BDCA.
 * 07 DACB.
 * 07 BD.


 * The pairwise matrix looks as follows:


 * A:B=51:49
 * A:C=45:48
 * A:D=58:42
 * B:C=35:65
 * B:D=75:25
 * C:D=40:60


 * The CDTT set is A. However, Ranked Pairs(winning votes) chooses C. Markus Schulze 21 Jun 2005


 * Thanks. KVenzke 13:53, Jun 22, 2005 (UTC)

SSD vs. CSSD
An anonymous editor keeps changing this article (and others) to read that SSD is another name for Schulze. For example, s/he writes "where the method is also called "SSD", "CSSD", and "beatpath"" on various external resources, and reverts any attempts to remove "SSD" from that list. The first paragraph reads "The Schulze method is also known as ... "Schwartz Sequential Dropping" (SSD) ..."

In my opinion, this is incorrect. SSD has a different stopping rule from Schulze. Schulze stops when there are no cycles in the GOChA set. SSD stops when there is an undefeated candidate. In some examples Schulze and SSD can give different results.

I'd like to discuss and reach a consensus on this matter before I make any more edits. I would not like any more edits on this topic from anonymous users. Markus, since this page is named after you, your opinion might carry a bit more weight than the rest of us. Do you think that it makes sense to say "The Schulze method is also known as SSD?" Thank you. --Hermitage 7 July 2005 06:15 (UTC)


 * Well, a potential Schulze winner is a candidate A with p[A,B] >= p[B,A] for every other candidate B. A potential SSD winner is always also a potential Schulze winner. Therefore, SSD is a Schulze method. Markus Schulze 7 July 2005


 * In my opinion, that's a confusing way to put it, but since the page is called "Schulze method", I will not argue with you, unless a lot of other people agree with me. --Hermitage 8 July 2005 06:05 (UTC)


 * In my opinion, Mike Ossipoff's terminology is more confusing.


 * Suppose X1 and X2 are two election methods. Suppose the set of potential X1 winners is always a (not necessarily strict) subset of the set of potential X2 winners, so that being a X1 winner implies being a X2 winner. Then, in my opinion, it can hardly be said that X1 and X2 were two completely different methods. I would rather say that the X1 method is a X2 method. However, according to Mike Ossipoff's terminology, X1 and X2 are two completely different election methods even when both methods always choose the same candidate with the same probability. For example, he wrote that "BeatpathWinner and CSSD" were "equivalent, but completely different".


 * By the way, here you wrote about Ranked Pairs and MAM: "I read the definition of MAM on his web site a year or so ago, and I had to ask on the EM list whether it was equivalent to RP. Thus, if MAM is discussed at all on wikipedia, I'd like for it to be made clear that it is a particular version of RP, or an alternate name for RP."


 * It is rather inconsequent to say, on the one side, that MAM is only a "particular version" of RP or even only an "alternate name" for RP and, on the other side, that SSD and Schulze were two completely different methods. Markus Schulze 8 July 2005


 * Yes, I would say that SSD is a variant of Schulze, but I wouldn't say that Schulze is also known as SSD. I would say that MAM is a variant of RP, but I wouldn't say that RP is also known as MAM.
 * (An imperfect but possibly helpful analogy: I would say that an otter is a kind of mammal, but I wouldn't say that mammals are also known as otters.)
 * By saying that SSD and Schulze are different methods, MO seemed to be saying that he or someone else could take credit for SSD independently of Schulze. I am making no such argument. I am simply trying to avoid confusion that may arise from the statement "Schulze is also known as SSD." --Hermitage 9 July 2005 08:45 (UTC)


 * SSD is a Schulze method, because a potential SSD winner is also always a potential Schulze winner. At your website, you also discuss SSD. It isn't clear why you don't want these facts to be mentioned at the "Schulze method" site. Markus Schulze 27 July 2005


 * For me, this is a semantic issue rather than an attribution issue. I've tried to explain my opinion above. I appreciate that you are making the change while logged in as yourself; I believe that previously you had reverted similar edits of mine as an anonymous user, leaving me puzzled. --Hermitage 10:01, 27 July 2005 (UTC)


 * At your website, you first discuss SSD in special (setion I.B.3.d) and then you discuss the Schulze method in general (section I.B.3.e). I guess you do this because of didactic reasons: When the Schulze method is already known, then there is actually no use anymore to discuss SSD in special.


 * However, this is only a didactic trick to circumvent the need to explain why you discuss SSD at all at your site. Markus Schulze 27 July 2005

Why All the Criteria?
Just curious why the lengthy list of satisfied and not satisfied criteria in this article, which seems to be the POV exception to what has been agreed upon in other articles. Should this criteria be trimmed down to what is standard with other voting method articles?--Fahrenheit451 01:02, 27 July 2005 (UTC)


 * That is one option. Another option is this: Maybe we could go back to the talk:Voting system/Included methods and criteria page, and agree on both a long list and a short list of criteria. The long list could look more like the Schulze method page, and the short list could be the one that we've agreed on so far. Then, it would be at editors' discretion at a page-by-page basis to choose between the long and short lists. --Hermitage


 * I don't buy into the long and short list notion. Let's keep it simple and be consistent.--Fahrenheit451 01:31, 27 July 2005 (UTC)


 * Using lists of different length, it is possible to have consistency while allowing for different levels of depth in criteria sections. It is different from simply picking and choosing criteria you like for a particular page. --Hermitage 01:37, 27 July 2005 (UTC)


 * By the way, I am open to the addition of these criteria to other method pages: mutualy majority, Pareto, Smith, Schwartz, Woodall's plurality, and invulnerabilty to burying. --Hermitage


 * MM is specific to majoritarian methods. Smith and Schwartz are specific to condorcet methods. I don't know of any voting methods that don't satisfy Pareto, so that is unnecessary for comparison.  Woodall's plurality is esoteric.  So, that will not fly.--Fahrenheit451 01:31, 27 July 2005 (UTC)


 * I am open to the deletion of these criteria from this page: strategy free criterion, generalized strategy free criterion, strong and weak defensive strategy criteria, minimal defense, favorite betrayal criterion, summability. --Hermitage 01:20, 27 July 2005 (UTC)


 * Let's be fair and consistent.--Fahrenheit451 01:31, 27 July 2005 (UTC)


 * If you want some criteria to be not used anymore, then you should call for a vote for deletion of this site. But you should not simply behave as if you had successfully run such a vote. Markus Schulze 27 July 2005


 * Markus, are you being sarcastic? Please tell me who has behaved as if successfully getting a vote consensus for site deletion. Frankly, I like your method and would oppose deletion of the article.  My interest, which I think is shared by other editors here, is to have a consistency of method criteria in the articles. In fact, I would strongly encourage you to set up a website devoted to your method in detail and perhaps a blog on it and related topics. --Fahrenheit451 16:23, 27 July 2005 (UTC)


 * In my opinion, one can vote to exclude criteria from method pages without formally voting to delete the page of the criterion itself. This is the aim of the talk:Voting system/Included methods and criteria page. In my opinion, the former approach is a less drastic way to keep the "mainstream" articles clean, and so I support it. --Hermitage 09:54, 27 July 2005 (UTC)

Actually, I would not oppose having a dual list system AS LONG AS: 1. The standard list is always featured prior to the optional second and on every method article. 2. The exhaustive list is a supplement to the standard list and does not repeat criteria in the first and the criteria must be published and peer-reviewed. That would include, in this case, internet publication.--Fahrenheit451 16:32, 27 July 2005 (UTC)


 * Dear Fahrenheit451, sorry for my sloppy formulations. I didn't mean to say that there should be a vote for deletion for the Schulze method article. I meant to say that when Hermitage wants to delete all links e.g. to the summability criterion article then it would be more in accordance with Wikipedia's editing policy when he calls for a vote for deletion for the summability criterion article before he deletes those links. Markus Schulze 27 July 2005


 * I would not support deleting the summability criterion article, but rather just removing the mention in the basic criteria statements in the article. It would be o.k. putting it in an exhaustive list.--Fahrenheit451 21:25, 27 July 2005 (UTC)


 * If an article is agreed to be unworthy of having a place in the mainstream of the voting theory category, I personally prefer to delete links to the article rather than deleting the article itself. I prefer the former approach because it is less destructive, more readily reversible (I assume), and because it does not entirely waste the effort of those who worked on the article in the first place.
 * However, if faced with an all-or-nothing ultimatum, there are some articles such that I would rather delete them altogether than routinely link to them from voting method pages. These articles include strategy free criterion, generalized strategy free criterion, strong and weak defensive strategy criteria, minimal defense, favorite betrayal criterion, and summability. --Hermitage 03:45, 28 July 2005 (UTC)


 * Dear Hermitage; in effect, it is the same whether an article is deleted or whether all links to this article are deleted. So if you think that an article is "unworthy of having a place in the mainstream of the voting theory category", then you should call for a vote for deletion of that article, but you should not simply behave as if you had successfully run such a vote. By the way: The weak defensive strategy criterion and the strong defensive strategy criterion just survived votes for deletion.
 * Furthermore: Whether all links e.g. to the summability criterion article should be deleted, should be discussed at Talk:Summability criterion and not at Talk:Schulze method or Talk:Borda count or Wikipedia talk:WikiProject Voting systems/Included methods and criteria. Markus Schulze 28 July 2005

I have to object to the exceptional treatment this method gets in relation to others here on wikipedia. Most of the method criteria would be deleted by people like Hermitage if it were used on other methods. This is highly discriminatory and POV.--Fahrenheit451 16:58, 9 August 2005 (UTC)


 * As long as a criterion has an article, it isn't POV to mention in the article of an election method whether this election method satisfies this criterion. Markus Schulze 9 Aug 2005
 * I agree with Markus, adding content such as which criteria it satisfies isn't POV as it adds encyclopedic information. This applies even if it may be relatively obvious or implied from other information, such as with the strong and weak defensive strategy criterion; see State the obvious. Scott Ritchie 21:08, 9 August 2005 (UTC)

That's fine. Then why all this inconsistent treatment on different method articles? I put summability criterion as satisfied by Borda count and Hermitage has a hissy fit and deletes it. I have no problem with you and Markus taking that point of view, but I say you should take it consistently: If an editor deletes satisfied voting method criteria that has an article from any method article, then you should object just as well.--Fahrenheit451 21:16, 9 August 2005 (UTC)
 * I haven't worked on those articles, however I will hold the position that all criteria are not necessarily immediately relevant enough to always be included in all articles, paritcularly when the article is rather long as it is because there's a whole host of encyclopedic information other than the voting criteria. This is not the case with the Schulze method - it was designed to comply with many criteria, and doesn't have much of a history or usage pattern outside that, hence there is little encyclopedic information other than the criteria.  This is slightly less true with articles such as Borda count and Single Transferable Vote, as there is a whole lot more to say about those subjects. Scott Ritchie 23:28, 9 August 2005 (UTC)

Scott, perhaps I am not duplicating what you just wrote: Am I right that you are stating 1. If a method has a history of use, then all relevant complying criteria should not be listed in the article? 2. Schulze method is the exception because it has not been used very much? You just contradicted yourself. Take a look at what you wrote before that: "As long as a criterion has an article, it isn't POV to mention in the article of an election method whether this election method satisfies this criterion. Markus Schulze 9 Aug 2005
 * I agree with Markus, adding content such as which criteria it satisfies isn't POV as it adds encyclopedic information. This applies even if it may be relatively obvious or implied from other information, such as with the strong and weak defensive strategy criterion; see State the obvious. Scott Ritchie 21:08, 9 August 2005 (UTC)"

Now, you either lied the first time, the second time or both: "adding content such as which criteria it satisfies isn't POV as it adds encyclopedic information.  This applies even if it may be relatively obvious or implied from other information" Listing satisfied criteria is either good for everybody or nobody, not just for a few of the self-ordained elites. Let's skip the bullshit Scott and get straight and honest.--Fahrenheit451 00:14, 10 August 2005 (UTC)
 * I'm not exactly sure where you think the contradiction in what I said lies, or why you seem to be taking a hostile attitude over this. I'm not arguing against you, I support relevant information making its way into the voting articles. All I'm really making a case for is a bit of condensing in articles that are already almost too long by focusing the criteria a bit; the Single Transferable Vote page already had to have its counting method sectioned off in summary style, and the Borda article may soon become too long as well if enough information other than all this hype about criteria ever makes its way in.  The Schulze article, from what I can tell, is in no danger of becoming too long like the STV article anytime soon simply because there isn't much else to talk about in regards to it.  Scott Ritchie 02:34, 10 August 2005 (UTC)

I shortened the Borda count article some time ago by creating the Nanson's method article and the Quota Borda system article. However, one cannot seperate the criteria from the method, and such criteria takes up little space. Long-winded explanations take up much space. In my opinion, such redundancies should be ruthlessly edited. I am fed up with a POV cabal coercing other editors on the voting method articles. What Markus stated is sensible. Let's apply that consistently to all voting method articles, O.K.?--Fahrenheit451 14:14, 10 August 2005 (UTC)

One possibility is to use the Schulze method criteria section as the template for all criteria sections for single winner methods. Who supports this; who is opposed to this? --Hermitage 11:18, 13 August 2005 (UTC)

And that is flagrantly POV towards a particular Condorcet method. No templates please.--Fahrenheit451 00:01, 17 August 2005 (UTC)

Uncovered Set
KVenzke argued that the Condorcet criterion and the Favorite Betrayal criterion are incompatible. Hermitage argued that the Condorcet criterion and invulnerability to burying are incompatible. Therefore, I added the uncovered set, so that there is at least one criterion that is violated by the Schulze method, compatible with the Condorcet criterion, and defined at Wikipedia or Electowiki. Markus Schulze 31 July 2005

Technicality
Please explain the heuristics and vote resolution process in terms that can be easily understood by a general audience, both for the benefit of the general public (if this voting method is proposed to replace an existing system, somewhere, this article should be comprehensible), and for the benefit of the Wikipedia community (there is a proposal to adopt this system for the Arbitration Committee elections). &#8227; &#5339;&#5505;  [ &#5200; ] 20:40, 10 November 2005 (UTC)

Illogic
One of the arguments for such a complicated system over something simple such as Approval voting is that groups of people can "target" candidates and not vote for them in an Approval voting system. Well, so what? That means they don't approve of that candidate. Which is the point of asking for their approval. If he were to win, they would oppose his policies as well, dunning his effectiveness. Otherwise, the individuals in the group should disapprove of the group, because the group disapproves of a candidate they approve of.

This all occurs in plural voting as well. And the Schulze method doesn't stop politicking from creating voting blocs. It just makes the math harder, and the bloc members less likely to do their own study and more likely to take the word of the bloc leaders as to which votes to cast...

--216.237.179.238 18:36, 7 December 2005 (UTC)

Heuristic
I'm having trouble with the use of the term 'heuristic' here, because it suggests a crude and unreliable approach as opposed to a watertight algorithm. Perhaps something like 'paradigm' would be a better choice here. -- Dissident (Talk) 16:01, 26 December 2005 (UTC)

Sincere expectation criterion
Dear Dissident,

suppose R1(X) is the number of voters who strictly prefer at least one other candidate to candidate X. Suppose R2(Y) is the number of voters who strictly prefer candidate Y to at least one other candidate.

Then Schulze(winning votes) satisfies the following two criteria:


 * Criterion 1: Suppose d[A,B] > R1(A). Then candidate B is elected with zero probability.
 * Criterion 2: Suppose d[A,B] > R2(B). Then candidate B is elected with zero probability.

The first criterion says that, when sufficiently many voters rank candidate A tied for top, then candidate B cannot be elected. The second criterion says that, when sufficiently many voters rank candidate B tied for bottom, then candidate B cannot be elected.

You claim that, when Schulze(winning votes) is being used, then it is always advantageous to give different preferences to the least preferred candidates. However, criterion 2 says that it can also be useful to give the same preference to the least preferred candidates. Markus Schulze 23:11, 22 February 2006 (UTC)


 * No, I already withdrew that too strong statement in Talk:sincere expectation criterion. Instead, I'm saying that given a uniform distribution over all possible rankings for each other voter, breaking the ties at the bottom gives a better expected benefit from the point of view from the voter. I also tried to give a proof for this there, for which I'd appreciate feedback from your side. -- Dissident (Talk) 01:22, 23 February 2006 (UTC)

I think it's hypocritical of you, Markus Schulze, to demand proof for assertions in the article as to whether a method satisfies or violates the SEC, while not holding yourself to the same standard. Otherwise you would have no problem with me simply removing any mention of it in the text. As it is, I have a proof by exhaustion that winning votes violates the SEC, although I was wrong in asserting margins satisfies it, because it turns out there is also a (lesser) incentive there to break bottom ties as to limit the number of co-winners. -- Dissident (Talk) 20:00, 28 February 2006 (UTC)


 * Dear Dissident, when someone introduces a criterion that is original research and then starts claiming that this method satisfies this criterion and that that method violates this criterion, then it isn't "hypocritical" to ask this person to explain his statements. Markus Schulze 12:25, 1 March 2006 (UTC)


 * Read again. The hypocrisy I'm referring to is a different matter, namely you making the article assert the compliance of Schulze with the SEC (regardless of strength measurement) without supplying proof, which you did here, here, here, here and here. -- Dissident (Talk) 16:18, 1 March 2006 (UTC)


 * Dear Dissident, I want you to remember that it is you who started making unverifiable statements about SEC and the different strength measures . Markus Schulze 16:44, 1 March 2006 (UTC)


 * When I did it, I supplied what I at the time thought was adequate support in the form of an informal proof, which you refused to critique and which I have now withdrawn based on my own findings with no thanks to you. But bringing that as an argument to excuse your reintroducing the criterion in the article (and not just moving it) seems to me like a petty form of retaliatory disruption. Only if you did it because you honestly believed Schulze satisfies the SEC in general, would it have been justified. -- Dissident (Talk) 17:35, 1 March 2006 (UTC)

Proof by exhaustion Minimax(winning votes) and Minimax(margins) violate the sincere expectation criterion
Assume there are 2 other votes (including possible "blank" votes). Then the following are all the cases where a change from A>B=C to A>B>C changes the set of winners:

Other voter 1: B=C>A Other voter 2: A=B=C Winners change from: A B C to: A B Change in utility: +1/6

Other voter 1: C>B>A Other voter 2: A=B=C Winners change from: A C to: A B C Change in utility: -1/6

Other voter 1: B>C>A Other voter 2: A=C>B Winners change from: A C to: A Change in utility: +1/2

Other voter 1: C>A>B Other voter 2: B>A=C Winners change from: A C to: A Change in utility: +1/2

Other voter 1: C>A=B Other voter 2: B>A=C Winners change from: A B C to: A B Change in utility: +1/6

Other voter 1: A=C>B Other voter 2: B>C>A Winners change from: A C to: A Change in utility: +1/2

Other voter 1: C>A>B Other voter 2: B>C>A Winners change from: C to: A B C Change in utility: +1/3

Other voter 1: A=B=C Other voter 2: B=C>A Winners change from: A B C to: A B Change in utility: +1/6

Other voter 1: B>A=C Other voter 2: C>A>B Winners change from: A C to: A Change in utility: +1/2

Other voter 1: B>C>A Other voter 2: C>A>B Winners change from: C to: A B C Change in utility: +1/3

Other voter 1: B>A=C Other voter 2: C>A=B Winners change from: A B C to: A B Change in utility: +1/6

Other voter 1: A=B=C Other voter 2: C>B>A Winners change from: A C to: A B C Change in utility: -1/6

Total change in expected utility: +3/169

-- Dissident (Talk) 20:00, 28 February 2006 (UTC)

CDTT (2)
If we're going to be consistently stringent here, then mention of Condorcet doubly-augmented top tier should also be removed from the article (for now) even if Woodall mentioned it a draft paper, because, as far as I know, it hasn't been officially published anywhere (yet). -- Dissident (Talk) 01:35, 8 March 2006 (UTC)

Schulze STV method
The links to Schulze STV method (the last two in External Resources > Original Writings) does not seem to belong in this article. The method should IMHO obtain a separate article containing those links and linked from here; though perhaps creation of a new article should be postponed until the method has been published. — JKľ 2006-04-06T11:42+0200

Assessment comment
Substituted at 22:03, 3 May 2016 (UTC)