Talk:Monotonicity criterion

message: There's a "message board argument" tone to many sentences in the latter half of the article.  "And not, as claimed by earlier versions of this wikipedia article, X" sounds childish.  —Preceding unsigned comment added by 24.84.44.227 (talk) 13:53, 5 January 2011 (UTC)
thread_title: Tone

message: I've removed text which stated that Single Transferable Vote can be non-monotonic depending on the methods used.  No counting method (not even Meek's method) eliminates the non-monotonicity of STV - all counting methods reduce to IRV in single winner elections, and IRV is non-monotonic.  Some counting methods, such as Meek's method, reduce the potential for tactical voting with STV, but they do not completely eliminate the non-monotonicity.
: I amnot sure I agree with the removal.  It is not enough to say that Meek's method cannot be montonic because 'STV' is never monotonic. That argument is circular. I will post a fuller answer at the STV talk page when I have researched it. Alan 09:46, 17 May 2005 (UTC)
replies: text:  When I added that text ("STV may or may not be monotonic, depending on the method used") I was actually thinking of Condorcet-STV, not Meek. Meek can be non-monotonic, though in real-world elections it is rare; see . Since Condorcet-STV doesn't actually tabulate vote transferral directly, it is not susceptible to the same analysis that indicts other STV systems; in some sense, Condorcet-STV is STV in effect, not in implementation. TreyHarris 15:25, 17 May 2005 (UTC)

text: Is there any proven statement that 'any' STV-method isn't monotonic? Like "any method that fulfills ... (which we call a 'STV-method') ... is not monotonic". Otherwise the most rigid statement should be "satisfaction of monotonicity criterion hasn't been proven for any known STV method". To write "all known STV methods are not monotonic" requires to show counter-examples for all of them. Please show me e.g. an example that Schulze STV is not monotonic. It reduces to the monotonic Schulze method in single winner elections, so any proposed counter-example must have at least two seats to be filled. Best, --Richard (talk) 11:52, 24 April 2014 (UTC)

text: "Clearly any voting system is non-monotic sometimes.". This is simply wrong. You might have written "Any voting system may be redesigned in some way (resulting in a different system), such that it becomes monotonic, or loses this property". Best, --Richard (talk) 11:33, 24 April 2014 (UTC)
thread_title:  STV is never monotonic 

message: In the example of a violation of the Monotonicity Criterion, it says that candidate C would be the Condorcet winner. However, it seems that there is no Condorcet winner in this case. In  pairwise matchups C would beat A, A would beat B and B would beat C, meaning all three would be in the Smith Set. The winner would then depend on what form of Condorcet voting would take place. I would suggest solving this problem by either
1) Changing the second preference of A's voters to C (this will create 4 categories in the second election, but still result in a violation of monotonicity). Then in pairwise voting we would have C beats A and C beats B, meaning C is not the Condorcet winner.
2) Remark that there is no Condorcet winner and choose an appropriate resolution scheme, such as Minimax Condorcet, to choose a winner.
--Anon.  18:25:07,  December 3, 2005 (UTC)
:I cut the sentence completely. Why discuss what Condorcet methods will do instead of, say, Bucklin voting? It seems irrelevant to the article. KVenzke 17:46, 4 December 2005 (UTC)
replies: text: Because condorcet methods pass the monotonicity criterion, that's why.  You're right that Bucklin voting should be mentioned as well.  The article could use more examples, such as a sentence explaining why Bucklin passes too.  Scott Ritchie 18:35, 4 December 2005 (UTC)
replies: text: Condorcet methods don't necessarily pass the monotonicity criterion. Consider Raynaud, Borda-Elimination (Nanson), or Smith//IRV. That's why it doesn't make sense to point out who the Condorcet winner is. KVenzke 04:16, 6 December 2005 (UTC)
replies: text: Can you point out an example demonstrating that?  It would be relevant to the article to show how they can fail. Scott Ritchie 00:10, 7 December 2005 (UTC)
thread_title:  Problem in the example? 

message: I have deleted the following sentence: "Most versions of the Single Transferable Vote which simplify to Instant Runoff when there is only one winner are not monotonic, however variants of STV such as CPO-STV and the Quota Borda system are." To the best of my knowledge, there is no STV method that has been proven to satisfy monotonicity. And the Quota Borda system has been proven to violate monotonicity. See example 3. Markus Schulze 09:22, 31 December 2005 (UTC)
replies: text: Why not CPO-STV, or other methods that simplify to monotonic systems when there is one winner? Scott Ritchie 04:07, 2 January 2006 (UTC)
replies: text: The Quota Borda system does simplify to a monotonic system when there is only one winner. Markus Schulze 09:50, 2 January 2006 (UTC)
thread_title:  Monotonic STV methods? 

message: The following sentence is incorrect:
Tactical voting in this way presents an obvious risk if a voter's information about other ballots is wrong, however, and there is no evidence that voters actually pursue such counter-intuitive strategies in non-monotonic voting systems in real-world elections.
''
I don't have the time or indeed the expertise to edit the section properly, but somebody should. The second clause ("there is no evidence" etc.) has been quite plainly wrong since the German federal election of 2005, in which conservative voters in Dresden deliberately voted against their party of choice (the CDU) in order to maximize that party's number of seats in the federal parliament. This was possible due to Germany's voting system (mixed member proportional with overhang seats) and the fact that the vote in Dresden took place a week after the rest of the country due to the death of a candidate, enabling voters in Dresden to vote tactically in full knowledge of the results already achieved elsewhere. As a result of this, the German Constitutional Court ruled on July 3 2008 that the German voting system must be reformed to improve its monotonicity.
For more, see:  (in English) or various German wikipedia articles such as   —Preceding unsigned comment added by 210.84.53.32 (talk) 04:19, 26 July 2009 (UTC)
thread_title:  Edit needed (by someone with more expertise than me) 

message: The stated IRV example is not very realistic, because it contains a Condorcet cycle among the three Candidates in election one, with a very strong support for any of the three majorities in the cycle. I also criticize, that the example assumes a huge swing of the voters preferences. I suggest another example, without a Condorcet cycle, and just a small swing:
Three candidates are running, a left, a right, and a center candidate. Hundred voters casting their ballots:
:
Number of votes	1st Preference	2nd Preference
28             	Right         	Center
5              	Right         	Left
35             	Left          	Center
32             	Center        	
The IRV-winner in that election would be Left, because Center gets eliminated first, and Left wins against Right according to the remaining preferences.
But if the five voters, who voted 1st LeftRight and 2nd RightLeft, switch their 1st and 2nd choice, then Right gets eliminated first, and Center wins against Left, so Left loses due to the new votes in favor of Left. -- Richard 13:45, 13 May 2011 (UTC)
replies: text: I corrected the error in the description of the example that's given here. In the article I used a different example. The two additional votes for Left in the article example (switching Right, Left, Center to Left, Right, Center) show a greater support for Left. That hurts Right in the first round, cause it no longer reaches the 2nd round. But Center, now entering 2nd round, beats Left. So the greater support for Left causes Left to lose, the result changes from Left winner, Right 2nd to Center winner, Left 2nd. Center is least prefered by the Left, Right, Center voters. Best, --Richard (talk) 10:53, 24 April 2014 (UTC)
thread_title: Instant-runoff voting  / Runoff voting (not monotonic) 

message: I altered the section on probability, chiefly because it read like someone making a case, rather than an NPOV statement of the available resources, some bits sounded like OR (The section  asked for a citation on still reads a little OR, but I think it deserves a chance to be substantiated).--Red Deathy (talk) 13:57, 7 June 2011 (UTC)
thread_title:  Probability 

message: The Muller–Satterthwaite Theorem relies on a definition of monotonicity that appears to be slightly different than the one presented here. Being more strict, it gives a much stronger result. Should the distinction be mentioned in this article? 2605:A601:A927:1900:257D:1C19:DCAC:E3EF (talk) 07:12, 17 November 2021 (UTC)
replies: text: It sounds relevant to the page, so yes. --Erel Segal (talk) 14:39, 18 November 2021 (UTC)
thread_title:  Muller–Satterthwaite Theorem