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Dear Michael Hardy, you wrote: "Would the authors of articles on voting methods please stop worshipping capital letters with such incredibly fanatical intensity. It makes it hard to get links right."
I consider your recent changes to be vandalism. If you are really so upset about capital letters, then it is sufficient to replace e.g. [[Ranked Pairs]] by [[Ranked Pairs|ranked pairs]]. But the way you replaced capital letters destroyed the links completely. -- Markus Schulze 5 Jan 2005
This article seems to define Ranked Pairs as using winning votes as the measure of defeat strength. Isn't that inaccurate, as far as what Tideman defined the method to be? KVenzke 17:42, May 22, 2005 (UTC)
Tideman prefers margins at present, and has probably assumed that margins would be the defeat strength definition when publishing articles about ranked pairs, although he is open to the idea of WV. I think that it makes sense to present both ranked pairs/Tideman and beatpath/Schulze as base methods that can work with different definitions of defeat strength. Hermitage 23:23, 8 Jun 2005 (UTC)
Most comments above are outdated. Some time after they were written, someone revised the Ranked Pairs article to mention only "margins of victory" (consistent with the way Tideman defined Ranked Pairs). It now makes no mention of the alternative (which MAM and several other methods use). On top of that, someone deleted the Wikipedia article about MAM. MAM satisfies more criteria than either Ranked Pairs or beatpath (Schulze) and there are some significant differences (and several subtle differences) between MAM and Ranked Pairs. Deleting the MAM article without merging its information into the Ranked Pairs article looks like vandalism, an attempt to suppress information about the best voting method. SEppley ( talk) 16:29, 8 March 2010 (UTC)
I think that it is somewhat confusing for Steve to refer to his method as "MAM", rather than as a particular version of ranked pairs (which it is, essentially). 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. Rather than bringing up MAM on wikipedia as a specific method, it might make more sense simply to discuss the component parts of MAM (i.e. the WV defeat strength definition and different tie breaker) as separate issues within the range of "ranked pairs" methods. However, if someone wants to briefly mention MAM in the article as an alternate name, I don't mind. Hermitage 23:35, 8 Jun 2005 (UTC)
F451 has deleted the MAM and MMV external links from this page. My personal opinion is that the links are appropriate, but I do not feel strongly enough to revert the edit. Hermitage 23:13, 13 Jun 2005 (UTC)
I'm conflicted. I definitely don't think MAM and MMV are significant enough to be mentioned in an article's text on Wikipedia; I think that the external links are perhaps the one place they should exist. But I don't feel strongly enough either. And I don't hold F451 at fault for anything here - if he makes an edit that's so non-controversial and keeps the articles clean, what's the problem? RSpeer 05:42, Jun 14, 2005 (UTC)
I am the Steve (Eppley) who invented and named the Maximize Affirmed Majorities voting method (MAM). Above, Hermitage has it backwards: it is more confusing to use the name Ranked Pairs as a family of voting methods that includes MAM as just a variant than to treat Ranked Pairs and MAM as specific, different voting methods. MAM is significantly different. Ranked Pairs is the voting method defined by Tideman in 1987, and refined by Zavist & Tideman in 1989. Tideman did not define Ranked Pairs to be a family of voting methods. The most significant ways that MAM and Ranked Pairs differ are (1) MAM allows each voter's ranking of the candidates to be a "weak" ordering (allowing indifference) whereas Ranked Pairs expects "strict" orderings, and (2) when sorting the pairs or majorities into a "largest to smallest" order of precedence, Ranked Pairs measures the size of each pair coalition by subtracting the size of its opposing coalition (what some people call "margins of victory"), whereas MAM measures the size of each majority *without subtracting* the size of its opposing minority (what some people call "winning votes"). MAM was invented independently of Tideman's work. MAM was initially defined as the voting method that selects, from all possible strict orders of finish, the order of finish that minimizes the largest "thwarted" majority (in the minlexmax sense). While searching for a quick algorithm to find that order of finish, I was unaware of the relationship between Ranked Pair's algorithm and what I was looking for. (I experimented for months with several algorithms that did not work quite right but came close, which I described at the time in an ongoing series of emails to Mike Ossipoff. Mike was like me at the time: aware of Ranked Pairs but unaware of its relationship to MAM until after I discovered MAM's quick algorithm.) Originally MAM was named Minimize Thwarted Majorities since that is what I sought to do, but after discussion I renamed it Maximize Affirmed Majorities to emphasize the positive rather than the negative.)
I wish someone had asked for my opinion regarding these proposed changes before they wrecked the Wikipedia information about MAM. I invested a lot of time thinking about naming issues, and it's unlikely anyone else is as familiar with all the ways MAM and Ranked Pairs differ. One can only believe MAM isn't significant enough if he doesn't understand the ways it differs from the other methods. MAM satisfies more criteria than Ranked Pairs and more criteria than Schulze's beatpath. Computer simulations show that majorities rank MAM winners over beatpath winners more often than vice versa, and more voters over the long run rank MAM winners over beatpath winners than vice versa. MAM differs from Tideman's Ranked Pairs in some significant ways and several subtle ways, but the Wikipedia articles on Ranked Pairs and MAM (which I did not write) said so little about the details of either method that most readers were unaware of all the differences. SEppley ( talk) 17:20, 8 March 2010 (UTC)
This article lacks an evaluation based on criteria. Since RP is a condorcet method, listing whether or not it satisfies the Smith criteria would be relevant. I wonder if there are any volunteers for this?-- Fahrenheit451 00:29, 15 Jun 2005 (UTC)
Hmm, I guess we could just copy all the criteria over from Schulze method, since they'd be the same. But one note: If this article defaults to a margins interpretation (which I hope it doesn't, in fact), then the method won't satisfy Plurality criterion, Strong Defensive Strategy criterion, or Weak Defensive Strategy criterion. ...And I notice there is no article for Plurality criterion. Hmmmm. KVenzke 05:22, Jun 15, 2005 (UTC)
Kevin Venzke is mistaken above where he claims the Schulze method (a.k.a. beatpath) and the "winning votes" variation of Ranked Pairs satisfy the same criteria. Schulze's method fails Peyton Young's "local independence of irrelevant alternatives," which is satisfied by Ranked Pairs (regardless of whether it uses winning votes or margins) and by MAM. The winning votes variation fails Mike Ossipoff's Strong Defensive Strategy and Weak Defensive Strategy criteria (and Steve Eppley's Minimal Defense criterion, which is very similar to Ossipoff's Strong Defensive Strategy criterion) since according to Tideman each vote in Ranked Pairs is a strict ordering of the candidates; whereas MAM and Schulze allow weak orderings. Schulze's method fails Steve Eppley's "immunity from majority complaints," which is satisfied by the "winning votes" variation and by MAM. (I've distinguished MAM here because MAM differs in several ways from the winning votes variation of Ranked Pairs: 1. MAM allows each vote to be a weak ordering, allowing voters to express indifference and save time by leaving candidates unranked or ranked equally worst. 2. MAM includes only the majorities when constructing the "largest to smallest" order of precedence, whereas Ranked Pairs includes all N*N-1 ordered pairs, including ties and minorities; note that ties can be larger than majorities in the variation of RP most similar to MAM, which uses winning votes and allows votes to be weak orderings; note also that, by including ties in the order of precedence, RP always constructs a strict order of finish by the time it has considered the smallest pair, whereas MAM postpones tiebreaking involving pairwise ties until a final stage (if necessary). 3. MAM's tiebreaker differs subtly from Tideman-Zavist's 1989 tiebreaker, allowing MAM to completely satisfy the strong Pareto criterion, which is not completely satisfied by the winning votes variation of RP.) SEppley ( talk) 18:28, 8 March 2010 (UTC)
Do the Ranked Pairs variants, Maximize Affirmed Majorities and Maximum majority voting, deserve their own article (especially given the amount of overlap due to the Tennessee voting example)? My vote is no. -- Dissident ( Talk) 23:21, 25 December 2005 (UTC)
Can anyone add a description of the weaknesses of this method? What kinds of strategic nomination / voting is it suceptible to? -- Doradus 21:50, 6 January 2006 (UTC)
The link in the Criteria section to the voting criteria table appears to be broken. It links an anchor on the Voting system page, but there does not appear to be any voting criteria table on that page. Qutezuce 08:56, 16 January 2006 (UTC)
I ask this as a layman. -- nyenyec ☎ 16:11, 10 February 2007 (UTC)
Well, as you can see from the discussion above, voting theorists tend to capitalize everything, sometimes to the point of silliness. But the decapitalized title "Ranked pairs" doesn't seem right to me; it makes it sound like the article is about a kind of pairs, instead of about a voting system referred to by the name "Ranked Pairs". In comparison, the Borda count really can be described as a "count", as it's a way to count up votes. rspeer / ɹəədsɹ 11:03, 11 February 2007 (UTC)
I started a discussion recently on the election-methods mailing list about how to determine "second place" in a Ranked Pairs election. An interesting fact I found is that in ranked pairs the second place winner can be determined either by looking at whomever is second in the (complete) graph OR by removing the winner from all ballots and rerunning the algorithm -- both will produce the same result. Scott Ritchie ( talk) 22:03, 14 October 2008 (UTC)
Note also that Ranked Pairs is equivalent to the voting method defined as the method that finds the "best" possible order of finish, assuming "best" is defined to mean the order of finish that minimizes the largest reversed pair, where the size of a pair "x ahead of y" is measured by the so-called "margin of victory": subtracting the number of votes that rank y over x from the number of votes that rank x over y. (By "minimizes the largest" I mean in the lexical sense. Any two orders of finish can be compared by considering only the pairs on which they disagree; that is, all pairs x,y such that one order of finish places x ahead of y and the other order of finish places y ahead of x.) If 51 voters ranked x over y and 49 ranked y over x, the size of the "x over y" pair is 2, and the size of the "y over x" pair is -2. (Margin of victory is a misleading term, since it can be positive, zero or negative, and it is unnecessary to use the term.) My point here is that Ranked Pairs already returns an order of finish, making it unnecessary to use Ranked Pairs iteratively to construct the rest of the order of finish. SEppley ( talk) 16:01, 8 March 2010 (UTC)
The result of the move request was: page moved per request. GTBacchus( talk) 04:01, 2 June 2010 (UTC)
Ranked Pairs →
Ranked pairs — This doesn't seem to be a proper noun. It's uncapitalized both in the
source publication as well as
this external link.
Jafeluv (
talk)
17:01, 25 May 2010 (UTC)
In the method of Ranked pairs candidates are divided into pairs & voters have to choose the winner of each pair. What if the number of candidates is odd? That must be a serious drawback of this voting method. Nikolay95 ( talk) 20:28, 13 September 2012 (UTC)
In the Example section, the subsection Summary follows subsection Ambiguity resolution example, yet the Summary subsection summarizes all subsection preceding Ambiguity resolution example without mention of the Ambiguity one. The Ambiguity resolution example subsection is effectively a second example, with separate example items (A>B>C>A as opposed to the Tennessee cities in the rest of the main section). It would seem appropriate to move the Summary subsection before the Ambiguity resolution example subsection. Anyone have a reason in opposition to this? — al-Shimoni ( talk) 16:17, 17 November 2012 (UTC)
Is there any algorithm which calculates a Ranked Pairs ranking in parallel? The algorithm in Eppley's MAM procedure definition paper is sequential. Wat 20 18:05 16 February 2013 (UTC)
72.68.72.137 ( talk) 04:38, 8 October 2014 (UTC)
The following line is in the "Lock" section of the algorithm description: "One way to resolve this issue is to allow cycles if they are needed to resolve ties (i.e., if a single new edge would not create a cycle, but multiple tied edges would), and then define the winners as the resulting Schwartz set."
Where does this come from? There seems to be no citation given. Can anyone give further description? — Preceding unsigned comment added by TheShepherd7 ( talk • contribs) 04:06, 18 November 2017 (UTC)
"Procedure > Sort" states that:
The pairs of winners, called the "majorities", are then sorted from the largest majority to the smallest majority. A majority for x over y precedes a majority for z over w if and only if one of the following conditions holds:
1. Vxy > Vzw. In other words, the majority having more support for its alternative is ranked first.
2. Vxy = Vzw and Vwz > Vyx. Where the majorities are equal, the majority with the smaller minority opposition is ranked first.
However, I'm having trouble seeing how the second criterion could ever be possible if there are no indifference or unstated candidates, as in the example, because surely Vxy = Vzw would imply that Vwz = Vyx.
Further, under "An example > Sort", the following is stated:
Nashville (68%) beats both Chattanooga and Knoxville by a score of 68% over 32% (a tie, unlikely in real life for this many voters). Since Chattanooga > Knoxville, and they are the losers, Nashville vs. Knoxville will be added first, followed by Nashville vs. Chattanooga.
but this appears to be in direct contradiction with the given procedure; abbreviating Chattanooga, Knoxville, and Nashville with c, k, and n respectively, and letting x = z = n, y = k, and w = c, we have that Vnk = Vnc = 68%, and Vkn = Vcn = 32%, so neither criterion is satisfied, and thus neither majority can precede the other.
It seems like to have the conditions agree with the reason given, we need to add a third condition similar to "Vxy = Vzw, Vyx = Vwz, and Vwy > Vyw". Or is the reason given incorrect?
I also can't seem to find any sources that back up this procedure, so I can't tell if there is indeed an error or if I'm just misunderstanding it. The article states in reference #1 that the original article uses a different approach to ranking the strength of a victory. Edderiofer ( talk) 14:54, 10 September 2018 (UTC)
Hi, User:Beland and User:Colin.champion; I've noticed that in the past couple of days, you two have been editing and reverting the article over the typography of the article. To prevent edit-warring (see WP:WAR), I've created this section where you two can hopefully come to a consensus on the matter instead. Edderiofer ( talk) 17:28, 30 January 2022 (UTC)
The article now says
Alternatively, you can use the procedure above to pick the winner, make that candidate first place, drop them from the election (i.e. drop all comparisons/edges that include them), and then repeat the process.
Please supply a citation to a textbook or similar to support this. Absent support, this is too easily confused with original research. — Quantling ( talk | contribs) 18:59, 25 February 2023 (UTC)
Until the these recent edits (by Closed Limelike Curves ( talk · contribs)), the article emphasized how to rank all candidates from first to last, not merely how to choose the first. Shouldn't we be keeping the description for full ranking? — Quantling ( talk | contribs) 18:41, 23 February 2024 (UTC)
The river method is not a variant of ranked pairs. The river method and the ranked pairs method have different heuristics; the river method tries to find the "best" arborescence (according to its own definition for "better"), while the ranked pairs method tries to find the "best" complete digraph (according to its own definition for "better"). The river method and the ranked pairs method are not related; the ranked pairs method has been proposed by Nicolaus Tideman in 1987, while the river method has been proposed by Jobst Heitzig in 2004. The river method and the ranked pairs method find different winners (even when there are no pairwise defeats of equal strengths). The river method and the ranked pairs method have different properties; the river method satisfies independence of Pareto-dominated alternatives, while the ranked pairs method violates this criterion; the river method violates reversal symmetry and local independence of irrelevant alternatives, while the ranked pairs method satisfies these criteria. The current version of this article misleads the reader into believing that the river method satisfies all criteria that are satisfied by the ranked pairs method plus independence of Pareto-dominated alternatives. The fact that both methods might look very similar doesn't justify the claim that the one method is a variant of the other method. Markus Schulze 10:06, 16 May 2024 (UTC)
@ Closed Limelike Curves: It looks like the change from "Ranked pairs" to "Ranked Pairs" would need to be implemented as an actual page move rather than via {{DISPLAYTITLE}} or similar. And in light of the discussions above on exactly this topic, if you want such a change then I recommend that you propose the move rather than boldly making it. In the meantime, I recommend that we leave the article text references to these two words as they were. — Quantling ( talk | contribs) 18:38, 24 June 2024 (UTC)
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Dear Michael Hardy, you wrote: "Would the authors of articles on voting methods please stop worshipping capital letters with such incredibly fanatical intensity. It makes it hard to get links right."
I consider your recent changes to be vandalism. If you are really so upset about capital letters, then it is sufficient to replace e.g. [[Ranked Pairs]] by [[Ranked Pairs|ranked pairs]]. But the way you replaced capital letters destroyed the links completely. -- Markus Schulze 5 Jan 2005
This article seems to define Ranked Pairs as using winning votes as the measure of defeat strength. Isn't that inaccurate, as far as what Tideman defined the method to be? KVenzke 17:42, May 22, 2005 (UTC)
Tideman prefers margins at present, and has probably assumed that margins would be the defeat strength definition when publishing articles about ranked pairs, although he is open to the idea of WV. I think that it makes sense to present both ranked pairs/Tideman and beatpath/Schulze as base methods that can work with different definitions of defeat strength. Hermitage 23:23, 8 Jun 2005 (UTC)
Most comments above are outdated. Some time after they were written, someone revised the Ranked Pairs article to mention only "margins of victory" (consistent with the way Tideman defined Ranked Pairs). It now makes no mention of the alternative (which MAM and several other methods use). On top of that, someone deleted the Wikipedia article about MAM. MAM satisfies more criteria than either Ranked Pairs or beatpath (Schulze) and there are some significant differences (and several subtle differences) between MAM and Ranked Pairs. Deleting the MAM article without merging its information into the Ranked Pairs article looks like vandalism, an attempt to suppress information about the best voting method. SEppley ( talk) 16:29, 8 March 2010 (UTC)
I think that it is somewhat confusing for Steve to refer to his method as "MAM", rather than as a particular version of ranked pairs (which it is, essentially). 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. Rather than bringing up MAM on wikipedia as a specific method, it might make more sense simply to discuss the component parts of MAM (i.e. the WV defeat strength definition and different tie breaker) as separate issues within the range of "ranked pairs" methods. However, if someone wants to briefly mention MAM in the article as an alternate name, I don't mind. Hermitage 23:35, 8 Jun 2005 (UTC)
F451 has deleted the MAM and MMV external links from this page. My personal opinion is that the links are appropriate, but I do not feel strongly enough to revert the edit. Hermitage 23:13, 13 Jun 2005 (UTC)
I'm conflicted. I definitely don't think MAM and MMV are significant enough to be mentioned in an article's text on Wikipedia; I think that the external links are perhaps the one place they should exist. But I don't feel strongly enough either. And I don't hold F451 at fault for anything here - if he makes an edit that's so non-controversial and keeps the articles clean, what's the problem? RSpeer 05:42, Jun 14, 2005 (UTC)
I am the Steve (Eppley) who invented and named the Maximize Affirmed Majorities voting method (MAM). Above, Hermitage has it backwards: it is more confusing to use the name Ranked Pairs as a family of voting methods that includes MAM as just a variant than to treat Ranked Pairs and MAM as specific, different voting methods. MAM is significantly different. Ranked Pairs is the voting method defined by Tideman in 1987, and refined by Zavist & Tideman in 1989. Tideman did not define Ranked Pairs to be a family of voting methods. The most significant ways that MAM and Ranked Pairs differ are (1) MAM allows each voter's ranking of the candidates to be a "weak" ordering (allowing indifference) whereas Ranked Pairs expects "strict" orderings, and (2) when sorting the pairs or majorities into a "largest to smallest" order of precedence, Ranked Pairs measures the size of each pair coalition by subtracting the size of its opposing coalition (what some people call "margins of victory"), whereas MAM measures the size of each majority *without subtracting* the size of its opposing minority (what some people call "winning votes"). MAM was invented independently of Tideman's work. MAM was initially defined as the voting method that selects, from all possible strict orders of finish, the order of finish that minimizes the largest "thwarted" majority (in the minlexmax sense). While searching for a quick algorithm to find that order of finish, I was unaware of the relationship between Ranked Pair's algorithm and what I was looking for. (I experimented for months with several algorithms that did not work quite right but came close, which I described at the time in an ongoing series of emails to Mike Ossipoff. Mike was like me at the time: aware of Ranked Pairs but unaware of its relationship to MAM until after I discovered MAM's quick algorithm.) Originally MAM was named Minimize Thwarted Majorities since that is what I sought to do, but after discussion I renamed it Maximize Affirmed Majorities to emphasize the positive rather than the negative.)
I wish someone had asked for my opinion regarding these proposed changes before they wrecked the Wikipedia information about MAM. I invested a lot of time thinking about naming issues, and it's unlikely anyone else is as familiar with all the ways MAM and Ranked Pairs differ. One can only believe MAM isn't significant enough if he doesn't understand the ways it differs from the other methods. MAM satisfies more criteria than Ranked Pairs and more criteria than Schulze's beatpath. Computer simulations show that majorities rank MAM winners over beatpath winners more often than vice versa, and more voters over the long run rank MAM winners over beatpath winners than vice versa. MAM differs from Tideman's Ranked Pairs in some significant ways and several subtle ways, but the Wikipedia articles on Ranked Pairs and MAM (which I did not write) said so little about the details of either method that most readers were unaware of all the differences. SEppley ( talk) 17:20, 8 March 2010 (UTC)
This article lacks an evaluation based on criteria. Since RP is a condorcet method, listing whether or not it satisfies the Smith criteria would be relevant. I wonder if there are any volunteers for this?-- Fahrenheit451 00:29, 15 Jun 2005 (UTC)
Hmm, I guess we could just copy all the criteria over from Schulze method, since they'd be the same. But one note: If this article defaults to a margins interpretation (which I hope it doesn't, in fact), then the method won't satisfy Plurality criterion, Strong Defensive Strategy criterion, or Weak Defensive Strategy criterion. ...And I notice there is no article for Plurality criterion. Hmmmm. KVenzke 05:22, Jun 15, 2005 (UTC)
Kevin Venzke is mistaken above where he claims the Schulze method (a.k.a. beatpath) and the "winning votes" variation of Ranked Pairs satisfy the same criteria. Schulze's method fails Peyton Young's "local independence of irrelevant alternatives," which is satisfied by Ranked Pairs (regardless of whether it uses winning votes or margins) and by MAM. The winning votes variation fails Mike Ossipoff's Strong Defensive Strategy and Weak Defensive Strategy criteria (and Steve Eppley's Minimal Defense criterion, which is very similar to Ossipoff's Strong Defensive Strategy criterion) since according to Tideman each vote in Ranked Pairs is a strict ordering of the candidates; whereas MAM and Schulze allow weak orderings. Schulze's method fails Steve Eppley's "immunity from majority complaints," which is satisfied by the "winning votes" variation and by MAM. (I've distinguished MAM here because MAM differs in several ways from the winning votes variation of Ranked Pairs: 1. MAM allows each vote to be a weak ordering, allowing voters to express indifference and save time by leaving candidates unranked or ranked equally worst. 2. MAM includes only the majorities when constructing the "largest to smallest" order of precedence, whereas Ranked Pairs includes all N*N-1 ordered pairs, including ties and minorities; note that ties can be larger than majorities in the variation of RP most similar to MAM, which uses winning votes and allows votes to be weak orderings; note also that, by including ties in the order of precedence, RP always constructs a strict order of finish by the time it has considered the smallest pair, whereas MAM postpones tiebreaking involving pairwise ties until a final stage (if necessary). 3. MAM's tiebreaker differs subtly from Tideman-Zavist's 1989 tiebreaker, allowing MAM to completely satisfy the strong Pareto criterion, which is not completely satisfied by the winning votes variation of RP.) SEppley ( talk) 18:28, 8 March 2010 (UTC)
Do the Ranked Pairs variants, Maximize Affirmed Majorities and Maximum majority voting, deserve their own article (especially given the amount of overlap due to the Tennessee voting example)? My vote is no. -- Dissident ( Talk) 23:21, 25 December 2005 (UTC)
Can anyone add a description of the weaknesses of this method? What kinds of strategic nomination / voting is it suceptible to? -- Doradus 21:50, 6 January 2006 (UTC)
The link in the Criteria section to the voting criteria table appears to be broken. It links an anchor on the Voting system page, but there does not appear to be any voting criteria table on that page. Qutezuce 08:56, 16 January 2006 (UTC)
I ask this as a layman. -- nyenyec ☎ 16:11, 10 February 2007 (UTC)
Well, as you can see from the discussion above, voting theorists tend to capitalize everything, sometimes to the point of silliness. But the decapitalized title "Ranked pairs" doesn't seem right to me; it makes it sound like the article is about a kind of pairs, instead of about a voting system referred to by the name "Ranked Pairs". In comparison, the Borda count really can be described as a "count", as it's a way to count up votes. rspeer / ɹəədsɹ 11:03, 11 February 2007 (UTC)
I started a discussion recently on the election-methods mailing list about how to determine "second place" in a Ranked Pairs election. An interesting fact I found is that in ranked pairs the second place winner can be determined either by looking at whomever is second in the (complete) graph OR by removing the winner from all ballots and rerunning the algorithm -- both will produce the same result. Scott Ritchie ( talk) 22:03, 14 October 2008 (UTC)
Note also that Ranked Pairs is equivalent to the voting method defined as the method that finds the "best" possible order of finish, assuming "best" is defined to mean the order of finish that minimizes the largest reversed pair, where the size of a pair "x ahead of y" is measured by the so-called "margin of victory": subtracting the number of votes that rank y over x from the number of votes that rank x over y. (By "minimizes the largest" I mean in the lexical sense. Any two orders of finish can be compared by considering only the pairs on which they disagree; that is, all pairs x,y such that one order of finish places x ahead of y and the other order of finish places y ahead of x.) If 51 voters ranked x over y and 49 ranked y over x, the size of the "x over y" pair is 2, and the size of the "y over x" pair is -2. (Margin of victory is a misleading term, since it can be positive, zero or negative, and it is unnecessary to use the term.) My point here is that Ranked Pairs already returns an order of finish, making it unnecessary to use Ranked Pairs iteratively to construct the rest of the order of finish. SEppley ( talk) 16:01, 8 March 2010 (UTC)
The result of the move request was: page moved per request. GTBacchus( talk) 04:01, 2 June 2010 (UTC)
Ranked Pairs →
Ranked pairs — This doesn't seem to be a proper noun. It's uncapitalized both in the
source publication as well as
this external link.
Jafeluv (
talk)
17:01, 25 May 2010 (UTC)
In the method of Ranked pairs candidates are divided into pairs & voters have to choose the winner of each pair. What if the number of candidates is odd? That must be a serious drawback of this voting method. Nikolay95 ( talk) 20:28, 13 September 2012 (UTC)
In the Example section, the subsection Summary follows subsection Ambiguity resolution example, yet the Summary subsection summarizes all subsection preceding Ambiguity resolution example without mention of the Ambiguity one. The Ambiguity resolution example subsection is effectively a second example, with separate example items (A>B>C>A as opposed to the Tennessee cities in the rest of the main section). It would seem appropriate to move the Summary subsection before the Ambiguity resolution example subsection. Anyone have a reason in opposition to this? — al-Shimoni ( talk) 16:17, 17 November 2012 (UTC)
Is there any algorithm which calculates a Ranked Pairs ranking in parallel? The algorithm in Eppley's MAM procedure definition paper is sequential. Wat 20 18:05 16 February 2013 (UTC)
72.68.72.137 ( talk) 04:38, 8 October 2014 (UTC)
The following line is in the "Lock" section of the algorithm description: "One way to resolve this issue is to allow cycles if they are needed to resolve ties (i.e., if a single new edge would not create a cycle, but multiple tied edges would), and then define the winners as the resulting Schwartz set."
Where does this come from? There seems to be no citation given. Can anyone give further description? — Preceding unsigned comment added by TheShepherd7 ( talk • contribs) 04:06, 18 November 2017 (UTC)
"Procedure > Sort" states that:
The pairs of winners, called the "majorities", are then sorted from the largest majority to the smallest majority. A majority for x over y precedes a majority for z over w if and only if one of the following conditions holds:
1. Vxy > Vzw. In other words, the majority having more support for its alternative is ranked first.
2. Vxy = Vzw and Vwz > Vyx. Where the majorities are equal, the majority with the smaller minority opposition is ranked first.
However, I'm having trouble seeing how the second criterion could ever be possible if there are no indifference or unstated candidates, as in the example, because surely Vxy = Vzw would imply that Vwz = Vyx.
Further, under "An example > Sort", the following is stated:
Nashville (68%) beats both Chattanooga and Knoxville by a score of 68% over 32% (a tie, unlikely in real life for this many voters). Since Chattanooga > Knoxville, and they are the losers, Nashville vs. Knoxville will be added first, followed by Nashville vs. Chattanooga.
but this appears to be in direct contradiction with the given procedure; abbreviating Chattanooga, Knoxville, and Nashville with c, k, and n respectively, and letting x = z = n, y = k, and w = c, we have that Vnk = Vnc = 68%, and Vkn = Vcn = 32%, so neither criterion is satisfied, and thus neither majority can precede the other.
It seems like to have the conditions agree with the reason given, we need to add a third condition similar to "Vxy = Vzw, Vyx = Vwz, and Vwy > Vyw". Or is the reason given incorrect?
I also can't seem to find any sources that back up this procedure, so I can't tell if there is indeed an error or if I'm just misunderstanding it. The article states in reference #1 that the original article uses a different approach to ranking the strength of a victory. Edderiofer ( talk) 14:54, 10 September 2018 (UTC)
Hi, User:Beland and User:Colin.champion; I've noticed that in the past couple of days, you two have been editing and reverting the article over the typography of the article. To prevent edit-warring (see WP:WAR), I've created this section where you two can hopefully come to a consensus on the matter instead. Edderiofer ( talk) 17:28, 30 January 2022 (UTC)
The article now says
Alternatively, you can use the procedure above to pick the winner, make that candidate first place, drop them from the election (i.e. drop all comparisons/edges that include them), and then repeat the process.
Please supply a citation to a textbook or similar to support this. Absent support, this is too easily confused with original research. — Quantling ( talk | contribs) 18:59, 25 February 2023 (UTC)
Until the these recent edits (by Closed Limelike Curves ( talk · contribs)), the article emphasized how to rank all candidates from first to last, not merely how to choose the first. Shouldn't we be keeping the description for full ranking? — Quantling ( talk | contribs) 18:41, 23 February 2024 (UTC)
The river method is not a variant of ranked pairs. The river method and the ranked pairs method have different heuristics; the river method tries to find the "best" arborescence (according to its own definition for "better"), while the ranked pairs method tries to find the "best" complete digraph (according to its own definition for "better"). The river method and the ranked pairs method are not related; the ranked pairs method has been proposed by Nicolaus Tideman in 1987, while the river method has been proposed by Jobst Heitzig in 2004. The river method and the ranked pairs method find different winners (even when there are no pairwise defeats of equal strengths). The river method and the ranked pairs method have different properties; the river method satisfies independence of Pareto-dominated alternatives, while the ranked pairs method violates this criterion; the river method violates reversal symmetry and local independence of irrelevant alternatives, while the ranked pairs method satisfies these criteria. The current version of this article misleads the reader into believing that the river method satisfies all criteria that are satisfied by the ranked pairs method plus independence of Pareto-dominated alternatives. The fact that both methods might look very similar doesn't justify the claim that the one method is a variant of the other method. Markus Schulze 10:06, 16 May 2024 (UTC)
@ Closed Limelike Curves: It looks like the change from "Ranked pairs" to "Ranked Pairs" would need to be implemented as an actual page move rather than via {{DISPLAYTITLE}} or similar. And in light of the discussions above on exactly this topic, if you want such a change then I recommend that you propose the move rather than boldly making it. In the meantime, I recommend that we leave the article text references to these two words as they were. — Quantling ( talk | contribs) 18:38, 24 June 2024 (UTC)