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Later no harm criteria?

This seems like an important criterion. Why is it not included in the chart and discussion? - 71.163.241.185

Later-no-harm criterion Indeed! My guess is LNH is uninteresting because only IRV/STV (and single seat plurality) support it. Tom Ruen (talk) 02:14, 23 September 2009 (UTC)

I didn't realize that. An inconvenient truth to some, I guess, but perhaps one Wikipedia shouldn't obscure? So people know what later-no-harm is, it's written up on the site: its key point is: "The later-no-harm criterion is a voting system criterion formulated by Douglas Woodall. The criterion is satisfied if, in any election, a voter giving an additional ranking or positive rating to a less preferred candidate cannot cause a more preferred candidate to lose." That seems important. -71.163.241.185

For many election methods, 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 Borda count and the MinMax method, because some implementations of these methods satisfy the later-no-harm criterion while other implementations don't.

Markus Schulze 01:17, 24 September 2009 (UTC)

Even so, it seems like it should be addressed rather than just avoid the topic. It's an important criterion and seems misleading to not include it. -71.163.241.185

I don't see how any interpretation could allow Borda count passing. Tom Ruen (talk) 05:14, 24 September 2009 (UTC)

Suppose C is the number of candidates. Then usually, a candidate gets C-1 points for each first preference, C-2 points for each second preference, C-3 points for each third preference, etc.. This definition for the Borda count violates the later-no-harm criterion.

However, this implementation of the Borda count satisfies the later-no-harm criterion: Suppose R is the number of candidates who are ranked by this voter. Then the candidate with the first preference gets R points, the candidate with the second preference gets R-1 points, the candidate with the third preference gets R-2 points, etc.. Markus Schulze 10:41, 24 September 2009 (UTC)

I don't get it. Let's suppose I rank three candidates. R is "3." My first choice gets three points. My second choice gets two points. Let's suppose my second choice defeats my first choice by one point. Didn't my ranking that second choice cause my first choice to lose by one point? If I instead had ranked only my first choice, then those candidates would have tied and my first choice could have won in a tiebreaker. ... Also my broader point is that Later-No-Harm belongs in the list. Its absence comes across like a political decision, not one reflecting the policy choices that a government or organization makes in choosing a system.71.163.241.185 (talk) 12:18, 24 September 2009 (UTC)

When you rank 3 candidates, then the candidate with your first preference gets 3 points, the candidate with your second preference gets 2 points, and the candidate with your third preference gets one point. When you bullet vote for only one candidate, then this candidate gets only one point. So a candidate cannot be harmed by casting an additional preference. Markus Schulze 14:19, 24 September 2009 (UTC)

Wow, that's an insane way to satisfy a criterion, but I suppose that implementation creates a counter incentive against partial rankings, and a HUGE advantage to voters who like many candidates! Tom Ruen (talk) 20:39, 24 September 2009 (UTC)

I see your point, Marcus, but agree with Tom. This would never fly. The criterion belongs in the list, comparing the systems as they basically are without bizarre, unlikely variations. 71.163.241.185 (talk) 03:57, 25 September 2009 (UTC)

The argument to include later-no-harm is persuasive. Those like Markus Schulze with a potential self-interest in not including it because it favors a system they may oppose, should be working harder to demonstrate their fairness by including it, with whatever footnoted caveats seem appropriate. If they know how to manage this chart, they should adjust the chart to include it —Preceding unsigned comment added by 12.130.118.1 (talk) 15:02, 3 January 2010 (UTC)

I would accept including later-no-harm, but without colors. There is considerable fundamental philosophical disagreement with whether later-no-harm, in itself, constitutes a desirable property. (ie, you could equally well call the reverse property the "compromise" property and tout it as a positive aspect.) 187.143.7.74 (talk) 19:18, 12 February 2010 (UTC)

I have added Later-no-harm to the chart, drawing as best I could on existing consensus. That consensus is based on the present discussion and the content of other, relevant Wikipedia articles, all of which I linked when I could. Jack (talk) 22:21, 15 February 2010 (UTC)

Good job. I reordered the columns. Note: By my reckoning, Minimax meets both Condorcet and LNH. I've heard that's impossible, but I think that people who say that are actually not thinking of the Condorcet criterion but the "Smith criterion" that requires a winner in the Smith set. I could be wrong here. Homunq (talk) 22:47, 15 February 2010 (UTC)

Note: above comment based on misinterpreting LNH. Homunq (talk) 12:44, 23 May 2010 (UTC)

It seems very odd to mark Plurality as compliant with Later No Harm when there is no option to specify a later preference? Surely it should be marked not applicable? —Preceding unsigned comment added by 78.105.167.241 (talk) 21:40, 12 March 2011 (UTC)

Would someone who claims it's important that Later No Harm be satisfied explain why it's important? In other words, explain the harm caused to society when it's violated, or show that violations will be exploited to produce winners that are worse or less accountable to the voters as a whole. If the justification is merely that some voters will sometimes have cause to regret they didn't misrepresent their preferences, it must be pointed out that satisfaction of LNH will not prevent voters from sometimes having cause to regret not misrepresenting preferences. For example, Instant Runoff satisfies LNH but voters would still have cause to regret when their failure to rank a compromise on top allows their least preferred alternative to win. I think it's fair to include LNH in the article, but only because so many other unimportant criteria are included. For more thoughts on the relative importance (or unimportance) of criteria, see the section below. SEppley (talk) 00:07, 12 March 2012 (UTC)

Color of the table for criteria pass/fail

There is a table in which the different voting systems each have their own row, and the different critera by which they are evaluated each has its own column. In this table, each cell is filled with a No or Yes, or in some cases a a more nuanced statement. The cells are color-coded, and that is the problem. The colors are so bleached so that it is hard to see the different between a very light red (No) and a very light green (Yes). I suggest that the colors are changed to stronger versions of those colors - I envision something like the red and green colors on the Italian flag.213.21.66.189 (talk) 15:49, 26 January 2012 (UTC)

I made all the colors twice as strong. 200.49.162.42 (talk) 02:07, 31 January 2012 (UTC)

Consistency/Participation of Random Ballot  Done

The criteria table states that "Random Ballot" fulfills the consistency and participation criterion, whereas "Random Winner" does not. Can anyone explain these two(/four) entries? I think the following is correct:

- "Random Ballot", Consistency: NO. If the voters are separated in two groups and in both groups a random-chosen ballot determines the same winner A, it doesn't mean that a random-chosen ballot of the combined voter groups will also determine A as winner. So, Random ballot doesn't fulfill consistency.

- "Random Winner", Participation: NA (or YES). Since the participation criterion explicitly needs the addition of ballots to produce a violation, "Random winner" can't ever violate this criterion. Since the criterion depends on ballots, but "Random Winner" doesn't know any ballots, it should be marked as not applicable.

Arno Nymus 134.102.209.204 (talk) 17:46, 8 March 2012 (UTC)

I think you're right. For RW/Participation, I'd go with NA. Be bold, make an edit you find reasonable. I don't think anyone really paid much attention to those cells before, and so I wouldn't look for too much logic behind what's in them now.

BTW, I agree with your edits removing the hedging from the Range/Approval/Participation/Consistency cells. I wouldn't be suprised if MarkusSchulze doesn't, though; as you can see from the talk page above, he's a stickler for which criteria are incompatible. In other words, if these systems pass Condorcet under Nash, then they fail Participation/Consistency under the same assumptions. Yes, that means people using logic like: "If voter x realizes that I prefer candidate A over B, she'll vote for C; so perhaps it's better that I just don't vote at all, and hope x realizes that", which I find implausible. But it's Markus's right to be a stickler if he wants to. Homunq (talk) 13:50, 9 March 2012 (UTC)

So, I changed it as discussed. Thx for your feedback. --Arno Nymus 77.23.79.151 (talk) 00:43, 10 March 2012 (UTC)

 Done -- Arno Nymus (talk) 17:53, 15 March 2012 (UTC)

Multiple-winner methods and consituencies

Do representatives in Multiple-winner election systems represent a constituency? How could they? They are not elected by a specific constituency. I mean, if some jurisdiction voted 100% for a party, say California voted 100% for the Democratic party for the Senate (using a multiple-winner method), how could a Republican be appointed to California's Senate seat and be considered to represent that constituency, ie. represent California? Int21h (talk) 23:41, 27 December 2011 (UTC)

The U.S. Constitution requires that U.S. Senate seats be filled in different years, which make those seats incompatible with multiple-winner methods -- which require filling the multiple seats using the same set of ballots.

Yes, a single representative cannot represent both Republican and Democratic voters. Double-size districts with a good multiple-winner method (I suggest VoteFair representation ranking) would elect one Republican and one Democrat. I think that would be fairer, but some people claim that larger districts make the representatives less "local" -- because they represent twice the area. VoteFair (talk) 19:42, 29 December 2011 (UTC)

While that is good information related to the subject of the hypothetical I advanced, it is unrelated to my underlying question regarding constituency representation in multiple-winner election systems. (This is why I am so loathe to give hypotheticals, because an answer may be related to the hypothetical but unrelated to the underlying question.) Int21h (talk) 14:20, 5 January 2012 (UTC)

If the voters give 100% support for only Democratic-party candidates, then a Republican cannot get elected. If you mean that the voters give 80% support for Democratic-party candidates, and a Republican candidate somehow gets elected to the second U.S. Senate seat, then of course the Republican Senator over-represents the 20% "constituency", and the Democratic Senator under-represents the 80% "constituency". If you are you asking a different question, please clarify. VoteFair (talk) 17:51, 6 January 2012 (UTC)

Yes, they can: California voters, in my hyopthetical, are not "the" voters, but only "some" (about 12%) of them. So no, I mean 100% of California voters (composing 12% of the national voters) voting Democratic, yet being represented in the US Senate by a Republican in national elections. Both my question and hypothetical probably imply a proportional or semi-proportional multiple-winner system, but I am not sure about this, hence I did not mention them. ("Jurisdiction" may have been misleading, but in the US the various states hold national elections, under state law, not the federal government, hence their are multiple voting jurisdictions. But "California's Senate seat", singular, should have implied I was referring to the US Senate as no state senate has only 1 seat, and therefore national elections.) Int21h (talk) 09:58, 7 January 2012 (UTC)

California (and each state) elects two U.S. Senators. (I'm the author of Ending The Hidden Unfairness In U.S. Elections, so I'm quite familiar with U.S. elections.) Under current conditions it is possible that California could elect one Democratic Senator and one Republican Senator, even with a strong Democratic bias. If a proportional (PR-like) election method were used to fill U.S. Senate seats, then some more U.S. Senate seats would have to be created, and one of those additional seats could be filled by a Republican who represents the (hypothetically?) few Republicans in California and also represents unrepresented Republicans in other states. If you are asking about a multiple-winner election method like STV (single transferable vote) -- which is not fully proportional -- then the results depend on how many seats are being filled, because anything beyond filling a first and second seat easily produces results that are unpredictable and unrepresentative. (Using a multiple-winner method to elect a single winner simply becomes a single-winner election.) VoteFair (talk) 17:26, 8 January 2012 (UTC)

Systems have been proposed which do give proportional results and also associate all representatives with districts. For instance, you could google "Balinski Fair Majority Voting" or "PAL representation". I don't think either of these systems have wikipedia articles yet. Homunq (talk) 13:53, 27 March 2012 (UTC)

Article lacks information about the relative importance of criteria.

The article presents quite a few criteria for comparing voting methods, but no info about which criteria are more important. It says only that there is disagreement about which criteria should be used. I think the article could be greatly improved by adding arguments why some criteria are more important than others.

My own point of view is that many of the standard criteria are relatively unimportant. For example, the so-called consistency criterion says that if 2 collections of votes produce the same winner, then the combined collection must produce that winner. Is it important? Since the rules can easily prevent a minority from partitioning the voters, minorities can't exploit scenarios where the voting method violates consistency, so that criterion seems quite unimportant compared to a criterion such as independence of clone alternatives. Tiny minorities can easily exploit scenarios where the voting method violates independence of clones, and they wouldn't even need knowledge of voters' preferences to successfully manipulate the outcome.

Also, a criterion that may be the most important of all isn't listed in the article. The work of many social choice theorists assumes the positions that candidates take on issues do not depend on the voting method; in other words, voters' preferences on candidates are wrongly assumed constant when comparing voting methods. In reality, candidates who want to win tend to take positions they believe will help them win, so positions do depend on the voting method. Some examples: The overly simplistic model in the Median Voter Theorem--two candidates, single issue with positions on a one-dimensional spectrum, single-peaked voter preferences--leads to a game-theoretic strategy where both candidates take the voters' median position. In a somewhat more realistic model, the two candidates know that additional candidates may enter the race, and this knowledge leads to a strategy where both avoid the median since if either takes the median it would create a winning opportunity for a third candidate; instead, one takes a position to the left and the other takes a position to the right. Another example is the system of partisan primary elections in the United States, which induces candidates to take positions that appeal to a segment of the voters (called the "base" of the party) who are not a representative sample of the general electorate, and who tend to defeat candidates who take median positions. Another example is the Borda voting method, where any platform of positions can be made to win regardless of the voters' preferences by nominating enough clones. With these examples in mind, the criterion I think is most important is that candidates who want to win should be induced to take positions that are accountable to the voters, even on issues that are not very important to the voters. (By accountable, I mean something along these lines: a position p on some issue is strongly accountable to the voters if no other position q on that issue is preferred over p by a majority, and a position p on some issue is reasonably accountable to the voters if, for all positions q on that issue that are preferred over p by majority, there exists a position r on that issue that is preferred over q by a majority at least as large.) Voting methods that perform well on this criterion would tend to settle issues on which the voters' preferences are settled, promote policy stability, reduce polarization, and reduce opportunities for wealthy special interest minorities to lobby/bribe their way to policies on "lesser" issues that large majorities would oppose. SEppley (talk) 23:22, 11 March 2012 (UTC)

The problem is that the importance of criteria is highly subjective. For example, IRV advocates highly appreciate the later-no-harm-criterion, whereas other people say that satisfying LNH only means to ignore important information. Also, there are different views about whether the only important thing about criteria is if their violation can be exploited for tactical voting (e.g. by adding candidates to steal votes; IIA, FBC) or if their violations also reveal unfair or unconstitutional flaws (e.g. that a vote is counted against the explicit will of the voter; Monotonicity, Participation). So both, IoC and Consistency are important - although, or maybe just because, they reveal qualitatively different problems of a voting system.

And last, but not least, there are objective differences of the importance of the criteria in relation to the ballots used. Best example is the "Mutual majority criterion". Both, Plurality and Range voting do not satisfy it. Plurality do not satisfy it because the voters do not have any chance to express on their ballots the information that is needed to fulfill MMC, thus Plurality itself does not have any chance to identify the winner, MMC considers best. So, for plurality the violation of MMC is a disadvantage. Instead of that, for Range voting it is the total opposite. Range Voting gives the voter not only the possibility to express the information the MMC uses to propose a winner, but even more information. And since Range voting uses this additional information in his process of assigning the winner (whilst the MMC does not), it sometimes leads to a better choice than the MMC and so "fails" it. So, Range voting "fails" the MMC since it has superior information, whilst Plurality fails it because it has inferior information. However, for voting system that have exactly the information the MMC uses, i.e. preferential-voting systems, it is a reasonable criterion.

Arno Nymus, 77.23.79.151 (talk) 22:18, 12 March 2012 (UTC)

Edit: I replaced "Majority criterion" by "Mutual majority criterion" in the last paragraph --Arno Nymus 77.23.79.151 (talk) 23:37, 12 March 2012 (UTC)

Granted the relative importance is subject to debate. One of my points is that the reader needs to see the arguments used in that debate in order to be able to judge which criteria are most important, and in which contexts the arguments apply. SEppley (talk) 17:19, 13 March 2012 (UTC)

I would like to have some pro- and contra-arguments on the according wikilinked criterion sites, but not in between of the short definitions. The later one would only limit the overview capabilities the table is made for. -- Arno Nymus (talk) 18:02, 15 March 2012 (UTC)

I agree that criteria-specific articles, not this article, should be where advantages (pros) and disadvantages (cons) should be explained. Note that trying to consolidate those advantages and disadvantages into a single scale of importance is impossible -- in a way that meets Wikipedia's requirement that such an importance ranking be appropriately referenced. VoteFair (talk) 18:08, 16 March 2012 (UTC)

I think that organizing the criteria into related sets at least helps in this regard. Whether a criteria relates to results, to voter guarantees, or to election administration will help the reader decide whether it is important. Maybe someone with greater wiki-fu than I have could put column group headers above the column headers... Homunq (talk) 13:35, 27 March 2012 (UTC)

I think that is a good idea. So, I added a row that depict the "criteria sets". --Arno Nymus (talk) 22:51, 27 March 2012 (UTC)

Yet another proposed column: "Equal rankings"  Done

• Allows equal rankings—Allows a voter to rank any two candidates equally at any position on the ballot. This can reduce the prevalence of spoiled ballots due to overvotes, and can give a less-dishonest alternative to some voting strategies.

Borda, IRV, Plurality, and Runoff would be red "No"; Minimax and Kemeny-Young would be white "Depends on variant used"; and all others would be green "Yes".

(The "less-dishonest alternative to some strategies" point is NPOV, not how I'd put it personally. Personally, I'd add some words to point out that dishonest strategies by more than one voter group can give pathological results desired by none, and so if there are semi-honest alternatives, that risk is significantly reduced.) Homunq (talk) 16:00, 15 February 2010 (UTC)

Kemeny-Young would be "yes"; it always allows "equal rankings". (BTW, the Kemeny-Young method does not have any variants that affect the input (votes) or output (results); the only variants are in how quickly the result is reached.) VoteFair (talk) 19:11, 15 February 2010 (UTC)

I changed the cell for Minimax to "Yes", since all three variants allow equal rankings. -- Arno Nymus (talk) 04:26, 23 March 2012 (UTC)

 Done --Arno Nymus (talk) 04:17, 13 April 2012 (UTC)

IIA/ISDA  Done

I approve the idea to add ISDA to the header and the criteria definition (instead of having it in every cell). However, IIA and ISDA are NOT incompatible. In fact, ISDA is a special case of IIA and IIA implies ISDA. Thus, I changed the column accordingly. --Arno Nymus (talk) 15:51, 29 March 2012 (UTC)

This is not true. (Although yes, it does sound intuitively right; I used to think the same thing myself.) Here's a proof. I know that a proof on a talk page is WP:OR, but I'm sure I can find a reference if you insist.

Take a voting system. If there is a CW, does someone else ever win? If no, then it is a Condorcet system, and does not pass IIA. If yes, then remove the winner. Add them back. They are smith-dominated by the CW, but they win. Thus the system does not pass ISDA. Thus, IIA and ISDA are incompatible.

Homunq (talk) 20:16, 29 March 2012 (UTC)

Also, splitting the cells plays hell with the sort key, since the column sorting only counts actual cells across to find a "column", ignoring colspan. The split cells in the LNH column were already fixed for that (not too hard because it's near the end of the rows) but your edit made a mess.

Please undo your edit, since you've made other (valid) edits since then. "IIA or <br>ISDA" should be one column, and the definitions should note their incompatibility. Homunq (talk) 20:32, 29 March 2012 (UTC)

Also please unsplit the polytime/resolvable cells. Yes, I know that we could move the sort keys around until it works, but that would be a maintenance nightmare for anyone who came later. It's bad enough with the split LNH cells; the only thing that makes that tolerable is that only two rows have an extra cell on net (Range and MJ) and because it's near the end of the row there's only one sort key that has to be moved for each. Homunq (talk) 20:42, 29 March 2012 (UTC)

You're right. I was misled by the thought that ISDA would be the same as IIA but for Smith-dominated alternatives. But in fact, it is totally not. It contains a strong absolute criteria and only a small part of a "candidate-related" one. I will correct the fault immediately. But, I'm thinking about changing the order of the criteria sets, so that ISDA could be positioned directly alongside the absolute criteria. What do you think about that? --Arno Nymus (talk) 23:18, 29 March 2012 (UTC)

I didn't readd links in every cell to IIA and ISDA, since the links are in the header. However, the definition of ISDA should be reformulated: 1. I propose to remove the term "cleary inferior". "Smith-dominated" will do fine. 2. If I am not mistaken, the current short description resembles "Schwartz-dominated", not "Smith-dominated". --Arno Nymus (talk) 00:19, 30 March 2012 (UTC)

As to moving the column: sounds like a good idea. Go ahead, we'll see how it works and adjust it if needed.

As to rewriting the ISDA definition: yes, be bold about wording. I do think though that that's correct for Smith dominated (with the "etc"; without that, it would be... something else, not quite Schwarz dominated, but yes, closer to Schwarz than Smith. Also, if you asked people to come up with a definition for "clearly inferior" that involved pairwise contests, they'd probably give Copeland, which also is more like Schwarz than Smith.) Anyway, give it a try, and again, if I don't agree, I'll say so. Homunq (talk) 02:26, 30 March 2012 (UTC)

I made the edit, feedback is welcome. --Arno Nymus (talk) 17:25, 30 March 2012 (UTC)

Great stuff. I especially like the trick of having more sort headers than column names. Perhaps we should do that for LNH and Condorcet/Majority Condorcet as well (Though "strategic yes" still makes a wide column :( .... and we'd have to change the bleedover LNH "No"s into "NA"s.)

Also, if you were motivated, you could make the "absolute" header bleed over halfway across the IIA/ISDA cells.

Homunq (talk) 18:01, 30 March 2012 (UTC)

But what's with the "local IIA" definition? I don't see that it adds anything.

1. "LIIA" was added by SEppley (2012-03-12). I just changed the sortation of the criteria (it was ordered behind IC, I moved it to IIA).
2. We could do the trick with the Majority/MMC column, if you don't have objections to giving Approval a "No".
3. The Condorcet column: I see the same problem, so I would like to leave it as is. (although I think, that the non-Condorcet Minimax method satisfies Majority Condorcet, without beeing mentioned in the table). --Arno Nymus (talk) 18:23, 30 March 2012 (UTC)

1. Good catch on the non-Condorcet minimax, I think you're right.
2. Approval "no" for MMC... well, I could imagine a counterargument, but it would be pretty absurd. OK, let's do it.
3. I think we should remove LIIA - it's not in the table, and it would be inevitably blank in several rows, since several systems lack a concept of "last" or "second".
4. Not sure what you mean by "same problem" for the (majority) condorcet column. "Strategic yes" is clearly true for the ones that have it, clearly not true for all others. I could understand an argument that "strategic yes" should get a light pink rather than a light green coloring, since it is short for "no, but strategically yes"; but... well, I'd still vote for light green.

Homunq (talk) 18:50, 30 March 2012 (UTC)

1. So, I will add the Minimax thing in the footnote and change the Majority/MMC column.
2. LIIA: I don't have an opinion on that. However, what you say, sounds reasonable.
3. The "same problem" just addressed the format problem "(Though "strategic yes" still makes a wide column :(" The content of the cells is definetely accurate, I just don't think that we can do the "column trick" for this column without makeing the table wider. ;) --Arno Nymus (talk) 19:11, 30 March 2012 (UTC)

So, there was a misunderstanding about Approval's No in the column. I meant "no" for both: Majority and MMC. --Arno Nymus (talk) 20:15, 30 March 2012 (UTC)

Yes, and I disagree with that. If you follow the link, it says "ambiguous" and explains why. Homunq (talk) 20:40, 30 March 2012 (UTC)

For some reason I know this explanation on the example page very well (and I know that it replaced a very biased one three weeks ago). However, in relation to that: what do you say about Condorcet loser criterion#Approval voting? --Arno Nymus (talk) 21:25, 30 March 2012 (UTC)

That's correct now as "no". But for MJ/participation, you could qualify the "no" with an argument similar to nb 8 (on MJ/consistency). How do you feel about that? Homunq (talk) 23:05, 30 March 2012 (UTC)

1. nb8 says that MJ satisfies "grade consistency" instead of consistency; I'm not aware, whether there is a MJ equivalent for participation.
2. Regarding the link to Condorcet loser: My point is that the argument there is essentially the same for the Majority criterion. --Arno Nymus (talk) 23:23, 30 March 2012 (UTC)

Right. On the other hand, you could extend the "ambig" argument to basically all the absolute criteria (including, I guess, ISDA, if you really pushed it.) So, where do we draw the line? To me, MC is clearly the right place. The MC is usually stated, as I've seen it, something like: "If a majority top-rank only A...". Certainly that's how we're interpreting it for MJ. This is not the same as MMC, Cond., Cond. loser, etc., which all (implicitly or explicitly) deal with more than two rankings. Approval passes MC in that sense. Basically, I think that we should make this "as voted" argument exactly once... not let it get in the way of the whole row, but give approval one chance to argue that. Homunq (talk) 23:39, 30 March 2012 (UTC)

OK, if we use the "top-rank"-definition for MJ, it is only fair to use it for Approval, too. So, I think this topic is completed. If there are no objections I will add a "done"-sign to this section in 5 days. --Arno Nymus (talk) 18:46, 31 March 2012 (UTC)

Good work. Homunq (talk) 20:54, 31 March 2012 (UTC)

 Done --Arno Nymus (talk) 00:30, 8 April 2012 (UTC)

approval/LNH

RRichie, you put a "No" instead of an "NA" for Approval in the LNH column. In approval, the only rating which is "later" than approved is unapproved. Marking another candidate unapproved of course can't harm an approved candidate, so, technically, the system passes the criterion, mathematically defined. Of course, I understand your argument that, if we were to look inside the voters head to see the preferences there, the system would not pass with regard to those preferences. Still, "No" is mathematically inaccurate. So, I think "NA" is more in the spirit of the criterion; but if you insist on having a value there, "Yes" is the only one that fits. (Note that the page previously included a definition of LNH which made approval fail. However, that definition was WP:OR; I replaced it with the definition from the source it already cited.) Homunq (talk) 18:52, 1 July 2011 (UTC)

Note that even by the uncited mindreading definition ("same-but-I-wish-it-was-later no harm"?) which RRichie apparently advocates, Approval passes later-no-help, just not later-no-harm. But I'm willing to leave an "NA" in the cell as a whole, rather than the "Yes/NA" which it would deserve.Homunq (talk) 19:31, 1 July 2011 (UTC)

I very much disagree. You are suggesting because a system doesn't allow a voter to indicate strength of preference except "0" or "1" that we can then assume voters have no sense of preference. But that is patently absurd. Consider a situation (a common one in minor variations) where you really like Candidate A, feel neutral about a second Candidate B and really dislike Candidate C. You are saying quite indefensibly that if I decide to approve of the first two candidates in order to try to defeat candidate C that my expression of support for Candidate B. For one academic discussion of such a situation, see Burr's Dilemma, discussed here: http://en.wikipedia.org/wiki/Burr_dilemma

It is not controversial to say approval voting fails to meet this criterion. Certainly it is central to the case against it in any real world debate -- and something any policymaker would understand immediately.RRichie (talk) 12:27, 2 July 2011 (UTC)

I've edited the page with a proposed resolution to this issue. Here's a copy:

	Major­ity/ MMC	Mono­tone	Consist­ency/ Particip­ation	Condorcet	Cond. loser	IIA	Cloneproof	Reversal symmetry	Polytime	Summ­able	Allows equal rankings	Later prefs	Later-no-help/ Later-no-harm
Approval	3Ambig­uous	1Yes	2Yes	4No	5No	3Ambig­uous	3Ambig.­	1Yes	1Yes	1O(N)	1Yes	No
Borda count	5No	1Yes	1Yes	5No	1Yes	5No	5No (teaming)	1Yes	1Yes	1O(N)	5No	1Yes	5No
IRV (AV)	1Yes	5No	5No	5No	1Yes	5No	1Yes	5No	1Yes	5O(N!)­	5No	Yes	1Yes
Kemeny-Young	1Yes	1Yes	5No	1Yes	1Yes	4No (but ISDA)	5No (teaming)	1Yes	5No	2O(N2)­	1Yes	1Yes	5No
Majority Judgment	1Yes	1Yes	4No	4No	4No	2Yes	1Yes	2Yes	1Yes	1O(N)­	1Yes	1Yes	3Yes/No
Minimax	2Yes/No	1Yes	5No	2Yes	5No	5No	5No (spoilers)	5No	1Yes	2O(N2)	3Some variants	1Yes	4No
Plurality	2Yes/No	1Yes	1Yes	5No	5No	5No	5No (spoilers)	5No	1Yes	1O(N)	5No	No
Range voting	5No	1Yes	2Yes	4No	5No	2Yes	3Ambig.­	1Yes	1Yes	1O(N)	1Yes	1Yes	5No
Ranked pairs	1Yes	1Yes	5No	1Yes	1Yes	4No (but ISDA)	1Yes	1Yes	1Yes	2O(N2)	1Yes	1Yes	5No
Runoff voting	2Yes/No	5No	5No	5No	1Yes	5No	5No (spoilers)	5No	1Yes	2O(N)­	5No	4No	2Yes
Schulze	1Yes	1Yes	5No	1Yes	1Yes	4No (but ISDA)	1Yes	1Yes	1Yes	2O(N2)	1Yes	1Yes	5No

Is this acceptable to you in its treatment of approval and LNH? Homunq (talk) 20:33, 2 July 2011 (UTC)

I definitely appreciate your effort here, but you're assuming that a voter has a simple "yes on equal level" to all" and "no to everyone else", and that kind of view of candidates in a multi-candidate racies is going to be the exception, not the rule. Unlikely plurality voting, approval voting gives you every opportunity to indicate a preference for a second choice who is much preferred to a last choice, but because it violates later-no-harm, you may well not do so and instead bullet vote for your first choice. So I think it's fundamentally misleading about the system to suggest it's in the same category as plurality voting. RRichie (talk) 22:28, 3 July 2011 (UTC)

Umm... I don't know what you want. The table as I've edited it makes a distinction between the mathematical definition of the criterion (what you've called my "assumption") and the practical meaning (basically, the thing you're arguing for). It gives priority to the practical meaning; the color of the relevant cell is red. It's only if you read the footnote that you get the quibbling about how the system technically passes the criterion.

I think that in your professional advocacy, you've grown accustomed to using the term "LNH" to refer to a practical argument, not a mathematical one. And I sympathize; I think I'm bending over backward to accommodate this. But in a section about mathematically-defined criteria, we can't completely abandon the mathematical definition given by the referenced source.

If you're willing to settle for the page as it is now, great. If not, please say or demonstrate specifically what you'd like to do to change it. I'm not Obama, I can't negotiate with myself forever.

Homunq (talk) 00:10, 4 July 2011 (UTC)

What I want is a return to the simple fact that approval voting violates the later-no-harm criterion in no uncertain terms. Note that Wikipedia's article states: "The criterion is satisfied if, in any election, a voter giving an additional ranking or positive rating to a less preferred candidate cannot cause a more preferred candidate to lose. You say the color is red, but you don't seem to leave the box blank, right?. I don't think you'e "bending backwards" to contradict common sense and Wikipedia's own article on later-no-harm. It's not "professional advocacy" that results in this understanding -- it's the simple fact that with approval voting you cannot give a positive rating to a less preferred candidate without counting against the chances of your more preferred candidate. RRichie (talk) 03:13, 5 July 2011 (UTC)

You're citing the definition from another wikipedia page, but Wikipedia is not a reliable source. The mathematical definition does not refer to an "additional" preference, but a "later" preference, as the source currently cited here in this article shows. And indeed, with the name "Later no harm", I can't really see how you could argue otherwise. Homunq (talk) 09:41, 5 July 2011 (UTC)

Amazing logic. To you the fact that with approval voting you can't indicate support for a second choice without it counting against your first choice means that anyone who doesn't indicate a second choice for that reason doesn't in fact have a second choice. I think the true test of meeting this criterion is what the sytems means when you DO have a disinct first, second and third choice. Please tell me how approval voting in such a situation allows you to indicate that fact. Furthermore, you should read the original source (the 1994 article cited for the defintion). This is what it says: "Later-no-harm. Adding a later preference to a ballot should not harm any candidate already listed." Can you please tell me how approval voting satisfies that criterion? RRichie (talk) 14:57, 5 July 2011 (UTC)

The key word there is "later".

Mathematical criteria do not deal with people and their preferences, they deal with sets, functions, and relations. I am sympathetic to your argument; sympathetic enough that I agree, I'd like to find a way for that cell to be red, as it is in my compromise proposal. If I were claiming what you say I am claiming, I would not be saying that. What I am saying is that we should find a way to reconcile the practical meaning of the criterion - on which you are correct - with the mathematical meaning it is given by the cited source - with which your only engagement is to recouch it in practical terms and then misattribute that as "my" position.

What is so wrong with the compromise I'm offering? 99% of people will never read the footnote, will just see a red square and infer that approval does not meet LNH. Those who do read the footnote will see that there's a technical debate, but that it is generally acknowledged that approval does not provide the practical guarantees that LNH is intended to ensure. In crafting that proposed compromise, I intended to convey nothing else; and I would welcome your edits intended to clarify this. But the simple fact is, that mathematically defined, a "later" preference means not the same preference level on the ballot, and so approval, technically speaking, passes that criterion; unless you can cite another definition (and yes, I'm sorry, but I will reserve the right to be picky about letting you cite FairVote promotional material on this matter, if I feel in good faith that such material is biased, and more importantly if it does not clearly lay out or refer to a precise mathematical definition), all your argumentation here constitutes original research. Homunq (talk) 17:46, 5 July 2011 (UTC)

How is the 1994 article that is the basis for the definition of the later-no-harm criterion original research? What does it have to do with "FairVote promotional material"? We're talking about a specific property of approval voting. It does not allow you to add a later preference to a ballot without that harming a candidate already listed." I guess this is the problem with Wikipedia -- no referees who can say "yes, the sky is blue" I'm done with this debate here, but I believe this (as well as the incredibly muddy presentation of approval voting in the main article on the subject) is a disservice to those seeking to understand the pro's and con's of different voting methods.RRichie (talk) 03:08, 7 July 2011 (UTC)

The 1994 article is not original research. It has nothing to do with FairVote. What it says is: "Adding a later preference to a ballot should not harm any candidate already listed." Approval does not allow adding a later preference; it only allows adding equal preferences. Therefore, it passes the criterion on a technicality. The current state of the page reflects that; a reader who does not care about technicalities will get the (practically right but not technically correct) impression that approval fails this criterion (and also Later-no-help, defined in a similar way).

I'm sorry you feel that this debate represents a failure of Wikipedia. Wikipedia certainly has failures, but I am convinced that in this case, a neutral referee would support me. ("In a context which requires precision, sometimes you must say that the sky usually appears blue, rather than saying that the sky is blue.") But please do not be discouraged. In the main approval voting article, we have a lot more space than one table row to explain things, and I'm sure you could help us do better; I'd invite you to make edits there. Homunq (talk) 13:33, 7 July 2011 (UTC)

You write "Approval does not allow adding a later preference; it only allows adding equal preferences." This is nonsense. The fact that the approval voting method is so unnuanced that it doesn't allow a voter to indicate strength of preference does not mean that voters in fact do not have strength of preference. So if I like A, am neutral on B and hate C, I cannot vote for B without it counting against A. This is crystal clear, yet you pull out a trick of saying "well, if a voter decides to vote for B, then that voter is saying that B is not a 'later preference.'" Again, simply nonsense.... I suppose by this definition you would say that range voting, which also violates is a system where indicating support for a second choice can cause a first choice to lose, violates LNH because of the voter's greater ability to indicate strength of preference. So in other words, a relative virtue for range voting becomes a vice.

I do not believe truly neutral referees could not support your position. They only could do do by accepting your solipsism that because a voter cannot indicate strength of preference, that voter in fact has no strength of preference.... What I would think would be a truly clear way to evaluate a system on this criterion is to establish a scenario (one that would exist in nearly all multi-candidates races in ther eal world) where voters have a range of preferences and see which systems allow voters to voter their interest - e.g, support their favorite to the maximum degree and oppose their least favorite to the maximum degree. Approval voting cannot do this, as you know, yet you not allow this limitation to be expressed. .. I truly hope you can see your position is indefensible and you need to allow this limitation to be indicated despite your advocacy for the method.RRichie (talk) 12:04, 9 July 2011 (UTC)

As I have said a number of times, I agree with you that, from a practical standpoint, approval's passing of LNH is nonsense. But it's a mathematical fact. Mathematical facts are often practical nonsense.

You propose a non-mathematical way to evaluate this criterion. I like your proposal, which could even be re-couched in a mathematically rigorous way (though it would be several times more complex than the mathematical formulation I've been relying on throughout this argument, and it would essentially amount to making a special case for approval so that it didn't pass). But unless you can find a source for your version of the criterion, we just can't use it.

Your bottom line is: "I truly hope you can see your position is indefensible and you need to allow this limitation to be indicated despite your advocacy for the method." As far as I can see, I am allowing this limitation to be indicated; the cell is red (as is the "later prefs" cell, which shows the "relative virtue for range voting" of which you speak). In fact, I thank you for bringing this issue up; I think the page is better this way than it was with "NA" as I had it before. So why are we still arguing? Homunq (talk) 12:43, 11 July 2011 (UTC)

Additional discussion: Approval/LNH again --Arno Nymus (talk) 07:41, 14 April 2012 (UTC)

Criteria Table: Ballot types column

I think, it would be reasonable to add a ballot type column to the criteria table, that describes what information the ballots used for the method possess.

For example Approval voting ballots contain approvals, i.e. a set of candidates that are approved by the voter;

IRV ballots are rankings, i.e. a endorelation which is transitive, anti-symmetric and every two not compared candidates are ranked "last" (that means for all candidates A,B,C (¬A>B and ¬B>A) implies (¬A>C and ¬B>C) )

Schulze ballots are simple orderings, i.e. endorelations. That means, Schulze method can easily handle rankings, but it does not need rankings. It outclasses IRV, since it also could handle if a voter only says "A>B and C>D, but I don't want to say whether I prefer A or C".

However, "rankings" and "orderings" are mostly referred identically as "preferential ballots".

Any objections against such a column? --Arno Nymus 77.23.79.151 (talk) 15:26, 10 March 2012 (UTC)

Adding the column is an excellent idea! I agree it's wise to clarify ballot-marking limitations/restrictions/ambiguities. Note that Wikipedia defines "ranking" in a way that allows equal ranking, which is regarded as a spoiled ballot in IRV. Wikipedia redirects "ordering" to the "order" article, which lists different kinds of ordering. So, the names used in the ballot-type column may need to be cleared up first. VoteFair (talk) 19:16, 10 March 2012 (UTC)

I looked around a little bit and came to the following results:

- ballots with only one candidate (plurality) are called "categorical" ballots [1]

- ballots for IRV/Borda can be called "strict rankings" [e.g. Tideman]

- ballots for Schulze etc. can just be seen as a set of "comparisons" (or in one term as an "endorelation", although it is a mathematical term). But looking "in the rush" didn't bring me any indication that anyone has researched using something other than "rankings" (strict or not strict) for these methods, although I read in some paper these days that forbidding preference cycles on a ballot because they are irrational would be a bad idea, since voters should not be banned from voting only for being irrational. That means that the idea of using non-ranking relations at least exists. Also, the construction of Ranked pairs and Schulze makes it totally obvious that they could handle a non-ranked set of comparisons without any change or problem.

I would just add a short description of each ballot type (categorical, approvals, (strict) rankings, comparisons, scores) before the table. Or in footnotes if this is preferred. -- Arno Nymus 77.23.79.151 (talk) 21:32, 10 March 2012 (UTC)

This is the explanation of the ballot types:

Ballot type: The voter have to state his choice in form of...

• ... a categorical choice of one candidate (e.g. "A is my favorite candidate.")
• ... approvals, i.e. a set of candidates the voter approves (e.g. "I approve candidates A, B and E.")
• ... a (strict) ranking, i.e. an list of candidates strictly ordered by the preferences of the voter (e.g. "A > B > E > D > H" or "I prefer A to B, B to E, E to D and D to H.")
• ... a set of comparisons (e.g. "A > B and E > H and H = C" or "I prefer A to B, E to H, and I think, H is equally capable as C, but I don't want to distinguish between A and E or A and H."). This is a generalized form of a ranking, so every voting system that can handle comparisons, also can be used if the ballots are rankings.
• ... scores, i.e. the voter gives cardinal values within in a certain range (e.g. 0-100) to each candidate (e.g. "A gets score 100, E gets 0, H 47, B 12 and D also 12") --Arno Nymus 77.23.79.151 (talk) 22:31, 10 March 2012 (UTC)

I suggest using "non-strict ranking" instead of "set of comparisons" because the comparison approach is never used on election ballots. (The fact that Condorcet methods can be used for search engines and other pairwise-comparison applications is irrelevant to elections.) Also I suggest using "plurality" or "single mark" instead of "categorical" because approval ballots are also "categorical", i.e. each candidate can be categorized as "approved" or "disapproved". Note that these suggestions are based on the need to choose appropriate words in the comparison table where the text-based descriptions won't fit, which means, for example, the column would be labelled "ballot type" (or "ballot") and the word "score" (not "scores") would be used for range voting. VoteFair (talk) 20:06, 11 March 2012 (UTC)

Now, I added the column to the table and the description into the descriptions of criteria above the table. So, you can see how it looks like. Additional feedback is welcome.

As you proposed, I changed "categorical" to "single mark".

Respective the "comparisons" I think, it looks quite good in the column, it is not significantly longer than "single mark", so I tend to leave it this way.

Respective "score"/"scores". I chose the plural "scores" since the voter gives one "score" to each candidate. But, if you think that this is incorrect, we can change it.

Thx for your feedback. --Arno Nymus77.23.79.151 (talk) 20:45, 11 March 2012 (UTC)

__removed done, see below__ --Arno Nymus (talk) 23:26, 16 March 2012 (UTC)

Thanks for adding the table column. The use of "ranking" ballots for IRV and "comparison" ballots for Condorcet methods doesn't make sense because both methods use ranking ballots, yet IRV imposes the added limitation of not allowing equal-preference markings. I suggest "full ranking" for IRV and "ranking" for Condorcet methods. Expressed another way, the name "comparison" ballot is ambiguous because, for example, approving and disapproving is also a form of comparison. (I'm open to alternatives if someone suggests an even better way to clarify the similarities and differences.) VoteFair (talk) 18:55, 18 March 2012 (UTC)

Thx for the feedback. I removed the "5 day-done". ;) I want to reply in three points:

1. Indeed, "approvals" are a form of "comparisons", but they are a limited(/special) form. This means: If you have approval ballots, you can use e.g. the Schulze method on them by interpreting the approvals as comparisons in the obvious way*. But the other way round is not possible. So, if you have some kind of comparisons, it is not possible to interpret them as approvals without "guessing". So, yes, approvals are comparisons, but comparisons are not approvals. "approvals" is a real subset of "comparisons".

*Obviously, this is not a proposal, but a mathematical fact. (The obvious way is: all approved ones are equals, all not-approved ones are equals, all approved ones are preferred over all not-approved ones.)

2. I think, a "full ranking" is a ranking that ranks all candidates, but as I understand, the ranking methods (IRV, Borda, Bucklin) allow to rank only the k best candidates and let the other candidates unranked. As you mentioned before, strict ranking is a good term for it. I therefore wrote "(strict) rankings" in the description, but for conciseness not in the table; but if you insist we can add the "strict" also to every cell in the table.

3. To see how the input for e.g. the Schulze method is defined I just took a look into "A New Monotonic, Clone-Independent, Reversal Symmetric, and Condorcet-Consistent Single-Winner Election Method". Schulze defines the input as a "strict weak order", i.e. a asymmetric, irreflexive, transitive and negatively transitive binary relation. So, this is a little bit more concrete than "comparisons", but also not as restrictive as (solely) rankings. I think, using the very restricting term "ranking" would hide the fact, that methods like Schulze and Kemeny-Young truly can handle much more than for example Borda count.

--Arno Nymus (talk) 02:31, 19 March 2012 (UTC)

Mmmm, yes, it's a dilemma. Currently I'm thinking that the word "pairwise" will fit on the first line and it's shorter than "comparison" on the second line, and all the affected rows are already two lines in height, so using "pairwise comparison" will not increase the size of any cell. That would be much better than using the ambiguous term "comparison" alone (in the table). (BTW, this naming is so much better than the phrase "preferential ballot" which is a strong contender for a prize for the most redundant phrase.) VoteFair (talk) 17:39, 19 March 2012 (UTC)

As you proposed, I changed "comparisons" to "pairwise comparisons". I think it's ok this way. --Arno Nymus (talk) 23:41, 19 March 2012 (UTC)

Much improved, thanks. I'll add that this morning it occurred to me that there is a voting/ranking method that literally does "pairwise comparisons" on a pair-by-pair basis. (Yes, it's tedious, but some people find that it helps them get a clearer understanding of who they actually prefer.) So, I suggest that we remain open to suggestions for a better naming convention. Personally I use the name "1-2-3 ballots," which came from a Canadian election-method reform advocate, Eduard Hiebert. Yet I realize that Wikipedia prefers academically oriented names, but that would take us to "preferential ballot" which is highly redundant and IMHO useless. So although the issue is resolved for now, I hope someone comes up with something better. VoteFair (talk) 20:24, 20 March 2012 (UTC)

Several points:

1. It seems to me that this column is almost entirely redundant with the 2 "affordances" columns. Since we can't really fit the columns we have, my first (weak) preference would be to remove it; or if not, to remove the "affordances" columns (which leaves us with the dilemma of how to fudge the approval/LNHarm cell, because it's technically a "yes" but effectively a strong "no".)

2. If we do keep this column, I'd prefer "ranking w/equality" to "pairwise comparisons".

3. Also, the Majority Judgment ballot is not technically a "score" ballot. The system is explicitly defined to use words, not numbers; thus I'd call it "graded". To highlight the similarity with range, perhaps "scores (grades)". I'd also accept just "scores" if we made this point in a footnote.

4. This column does not currently have a hidden sort key, so it sorts all wrong.

Homunq (talk) 13:42, 27 March 2012 (UTC)

Thx for the feedback. I realized 3. and 4. as proposed, moved the column "ballot type" to the "affordances" columns and added a row for the criterion sets as you proposed in the "importance" discussion. Since I have to leave for a meeting, I will add a reply on 1. and 2 later on. Please feel free to overview the footnote for Majority Judgment and the other changes. --Arno Nymus (talk) 16:38, 27 March 2012 (UTC)

ad 1.) You're right, that the information in the two affordances columns can be derived from the "ballot types" column. In fact, the other way round is not possible. There is additional information in the ballot types column that cannot be derived from the affordances column. That was the reason I proposed the ballot types column in the first place. So, the ballot types column is the more general information and the two affordances columns focus specific issues.

In fact, the columns for the "absolute" criterions also have similar redundancies: the Condorcet criterion implies the Majority criterion and a failure to the Majority criterion implies a failure to the Condorcet criterion. Although these two cases (ballot model/ absolute criteria) are not exactly the same, this shows that some redundancies are acceptable for clarity.

ad 2.) I would like to keep the information, that the "pairwise comparisons"-methods are capable of more than only not-strict rankings. If "pairwise comparisons" is not to be approved, it could also be renamed "a.t.i.n.t." for the above mentioned asymmetric, transitive, irreflexive and negatively transitive binary relation (with introducing the abbreviation in the description), but this would obviously mean that the reader have to read the description to understand it. So, I prefer the simple "(pairwise) comparisons". --Arno Nymus (talk) 22:48, 27 March 2012 (UTC)

re: 3 and 4: thanks.

re: 1... OK, if you prefer ballot types to affordances, that's OK. We should remove the affordances columns and give that info in the descriptions of the ballot types. Possibly we could also try to be tricky with the colors so as to convey the affordances info...

re: 2: it seems to me that "ranking"s relationship with "ranking w/equality" is far clearer than with "pairwise comparisons". "w/equality" does have the abbreviated "with", but other than that it seems perfectly clear that it is the same as ranking but (in your words) "allows non-strict rankings". Can you explain why you disagree with that? (Not why you like "pc" but why you dislike "r w/e")

Thanks again, Homunq (talk) 19:05, 28 March 2012 (UTC)

Hmm... having looked at the table again, I'd also be open to just compressing the affordances columns (fewer pixels). I'll try an edit to do that, see what you think. Homunq (talk) 19:16, 28 March 2012 (UTC)

(i) The compressed columns: I like it.

(ii) I "dislike" "r w/e" because it is very restrictive. This methods can handle much more than only r w/e, for example:

There are four candidates and I know, that A has some ability that B does not have and I know that C has some ability that D does not have, so I want to vote "A > B" and "C > D" (and I don't want to rank A > D or C > B, because I don't have a reason for that). The according methods (Schulze, Kemeny-Young, Ranked pairs etc.) have no problems with that. This would also match the definition of "a.t.i.n.t." (which is used defining the Schulze method). But "r w/e" would prohibit this. --Arno Nymus (talk) 20:29, 28 March 2012 (UTC)

OK, I finally understand you now. And I have to say: yes, the math works, but it seems highly implausible. What would the ballot even look like? How would you be prevented from voting cyclical preferences like A>B>C>A? (Yes, it's important to prevent this, because if you allow it it makes certain dishonest strategies much safer and thus more attractive.)

On second thought: don't answer that question. We're both skating the edge of WP:OR here. So it's probably safest to go with references. I've never seen a reference saying that the kind of ballot you suggest would be practical or even desirable. If you can produce one, I'll be happy to go with "pc". Otherwise, do you have any other objections to "r w/e"? Homunq (talk) 00:44, 29 March 2012 (UTC)

Only for your interest (without meaning for the discussion): One easy way for such a ballot would be to denote "X 1" for A and "X 2" for B, "Y 1" for C and "Y 2" for D on a normal preferential ballot like that on the image.

Now to the references:

• Arrow's "Social Choice and Individual Values" (http://cowles.econ.yale.edu/P/cm/m12-2/) uses "orderings fulfilling Axioms I and II", i.e. a "reflexive, transitive, fully-connected" binary relation (defined on pages 23, 13) with the meaning "at least as good as". This would allow my ballot example.
• Schulze's "A New Monotonic, Clone-Independent, Reversal Symmetric, and Condorcet-Consistent Single-Winner Election Method" (http://m-schulze.9mail.de/schulze1.pdf) uses a "strict weak order", i.e. an "asymmetric, irreflexive, transitive and negatively transitive binary relation" (defined on page 5) with the meaning "better than". This would also allow my ballot example.

Yes, understood. But your references just confirm that it works mathematically; your ballot proposal is WP:OR. Also, I'm pretty sure that such ballots could be used to make a burial strategy safer. Finally, your ballot proposal doesn't encompass all possible directed acyclic graphs. (And I shudder to think of the ballot spoilage issues if it did. "Sorry, that ballot is rejected, invalid XML.")

Separately, what do you think of my other recent changes: principally putting ISDA into the column head and definitions, and reformatting to tighten the column wrapping? Homunq (talk) 13:01, 29 March 2012 (UTC)

As said, the ballot proposal was only for your interest (and only for that one example). However, the references show that the methods are created for ballots that represent more than strict rankings. Obviously, "ballot" in "ballot type" means an abstract ballot used by the methods expressing only what information they provide, not the paper-equivalent of the real world, with the additional information how this information has been obtained (there are several ballots, which are used to get e.g. the score from a voter).

I support the general idea behind the ISDA changes, see the new IIA/ISDA section of the talk. --Arno Nymus (talk) 18:19, 29 March 2012 (UTC)

I still think, that we should use "comparisons" or something other that is strong enough to resemble the possibilities. But as long, as we use "rankings with equality", I think, "with equalities" can be erased from the table, since the next column besides the ballots is the "=ranks allowed"-column. Thus, as long as we use a term, that only differs because of the equality, the "=ranks"-column is enough to express that. So, I will change it that way. --Arno Nymus (talk) 00:31, 18 April 2012 (UTC)

Sounds good. I'd say that now you can mark this section "done" whenever you want. Homunq (talk) 00:57, 18 April 2012 (UTC)

Approval/LNH again  Done

Moving to a new section so the comments don't get lost. Here's the relevant comments by Arno Nymus and FilingPro copied from the Approval/LNH section above:

Addendum regarding the recent change done by ‎Filingpro (and why it was undone).

1. The former version more clearly explained the failure of (or more correctly not-applicability to) approval and plurality. Your version also removed the explanation for plurality completely.
2. The term "the current Wikipedia definition" should definitely not be used within an article.
3. Apart from that, please see this whole section for the background of the current version. --Arno Nymus (talk) 02:52, 13 April 2012 (UTC)

Thank you Arno Nymus for pointing out the need to avoid Wikipedia self-reference. I also agree with the goal of not deleting any information regarding plurality voting and its important distinctions. Q: Can you please clarify which mathematical definition of later-no-harm are you referring to for which approval is not applicable, and its source? Are you referring to Douglas Woodall's 1994 http://www.votingmatters.org.uk/ISSUE3/P5.HTM? — Preceding unsigned comment added by Filingpro (talk • contribs) 19:52, 13 April 2012 (UTC)

My response:

Yes, that one. Notice that Woodall starts out the paper by saying: "Each voter casts a ballot containing a preference listing of the candidates, which is written as (for example) abc, to denote that the voter places a first, b second and c third, with no fourth choice being expressed..." This is not how approval works; there isn't a single, unambiguous map from such an ordering to an approval ballot. Homunq (talk) 20:36, 13 April 2012 (UTC)

PS... in the above section, the eventual compromise was to merge the LNH cells with the ">2 ranks" cells when the latter were "No". That no longer works because of changes to how we do column sorting, so we put the "NA"s back. But we also made the left border of the NA cells invisible. Thus, we could just remove the text "NA" if that would be better. Homunq (talk) 20:48, 13 April 2012 (UTC)

I agree with Homunq and I want to add the following: "equal ranks" are not "later ranks". If one would consider equal ranks as "later ranks", this would mean that no reasonable voting method that allows equal ranks could satisfy "later no harm" (since for equal ranked A and B, the vote for A would have to be ignored to not harm B and the vote for B would have to be ignored to not harm A). --Arno Nymus (talk) 07:55, 14 April 2012 (UTC)

Thank you Homunq and Arno Nymus. I see my recent posting in the other area has overlapped your posting here. I have now moved it here...Filingpro (talk) 18:03, 14 April 2012 (UTC)

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REQUEST TO REOPEN CORDIAL DISCUSSION Filingpro (talk) 08:14, 14 April 2012 (UTC)

To all contributors: I have taken suggestions from Arno Nymus and carefully reviewed the arguments on this talk page, and examined Douglass Woodall’s 1994 document cited, and reopened discussion below. I hope that our contributors, who unanimously agree that approval clearly violates later-no-harm from a voter’s perspective, will be delighted to discover that there need be no contradiction in the framework of our original source, Douglas Woodall.

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A PROOF THAT APPROVAL MEETS WOODALL’S DEFINITION OF PREFERENCE ELECTION RULE Filingpro (talk) 08:14, 14 April 2012 (UTC)

See Woodall's 1994 http://www.votingmatters.org.uk/ISSUE3/P5.HTM

Woodall’s definition of preferential election rules allows for truncated preference listings, and how these truncations are treated is fully within the scope of the election rule.

Woodall defines the election rule that acts upon the optionally truncated profiles: “I define a (preferential) election rule to be a procedure that, given a profile, associates a corresponding non-negative probability with each outcome, in such a way that the probabilities associated with all possible outcomes add up to 1.”

Therefore, approval is a preferential election rule as defined by Douglas Woodall. To prove this, use any ballot that generates a truncated string of candidates deemed approved by the voter in any arbitrary order, and then perform an approval count on the marked candidates.

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END PROOF

Because Woodall’s definition of a preferential election rule includes approval, there is no basis for the claim that his use of the word “preference” excludes an “approval”. In other words, if approval is proven to be a subset of preferential election rules as defined by Woodall, it cannot be de facto exempt from the preferential criterion.

This conclusion is consistent with the observation the use of the word “preference” throughout the document is synonymous with the word “candidate”, and can be interchanged without changing any meaning.

Based on these new findings, I plan to update the voting criterion page as described briefly here, but will kindly wait for suggestions, improvements or counterarguments.

PROPOSED CHANGES

NO: later-no-harm (standard link to later-no-harm failing methods)

YES : later-no-help (no link - see explanation below)

Re: footnotes… Because there seems to be unanimous agreement that approval intuitively violates later-no-harm, I see no need to add footnotes/in the document for what has been deliberated on this talk page. Details about the later no harm method can be deliberated on the later-no-harm page.

Re: Plurality’s exemption to later-no-harm, I propose the following reference below…

Approval and Plurality do not allow later preferences. Technically speaking, this means that they pass the technical definition of the LNH criteria - if later preferences or ratings are impossible, then such preferences can not help or harm. However, from the perspective of a voter, these systems do not pass these criteria. Approval, in particular, encourages the voter to give the same ballot rating to a candidate who, in another voting system, would get a later rating or ranking. Thus, for approval, the practically meaningful criterion would be not "later-no-harm" but "same-no-harm" - something neither approval nor any other system satisfies

ADD: Plurality does not permit the voter to choose more than one candidate. Because no later choice can exist, then it is not possible to either help or harm a prior choice.

Re: later-no-harm summary in same document…

Later-no-harm criterion and Later-no-help criterion—... adding a later preference to a ballot will not harm/help any candidate already listed? Note that these criteria are not applicable to methods which do not allow later preferences; although such methods technically pass, they can be said to fail from a voter's perspective. ADD: Note that these criteria do not apply to methods which do not permit the voter to mark more than one candidate, such as <a href>Plurality</a>.

Thanks and I look forward to improving the page with everyone’s help.Filingpro (talk) 08:14, 14 April 2012 (UTC)

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Yes - Homunq I do see the argument regarding Woodall's reference to preferences in the listing. Please be patient as I respond to this concern. I believe what will be decisive in the end for this discussion is the procedural/algorithmic proof that approval remains a subset of the preference election rules set by Woodall. All that needs to be proved is this subset relationship exists, and then the fact that other preference rules use the ranking information is irrelevant. Does that make sense? I can elaborate more clearly if necessary. Thanks for the consideration. Filingpro (talk) 08:23, 14 April 2012 (UTC)

Further discussion follows below... Filingpro (talk) 10:29, 14 April 2012 (UTC)

Thank you for offering to remove the NA and substitute with blank although at the moment I do not yet consent as I have no yet been persuaded of the prior arguments that approval is exempt from application to later-no harm. I would like to first build consensus as to the determination of whether later-no-harm is applicable to approval through discussion.

I would like to suggest focusing our discussion on the procedural properties of the method rather than the semantic. I believe this would be helpful in clarifying the issue unambiguously. Please consider the following proof:

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EXPANDED PROOF THAT APPROVAL IS A PROCEDURAL SUBSET OF THE CLASS OF PREFERENTIAL ELECTION RULES AS DEFINED BY DOUGLAS WOODALL

Create a ballot in which a voter may mark or not mark each candidate on a ballot having a fixed, predetermined preference ordering of candidates (in arbitrary order). Perform an approval count on the resulting optionally truncated orderings.

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END PROOF

Because approval can be trivially expressed as a preference election rule by Woodall's definition, the preference criterion later-no-harm also applies.

Homunq and Arno Nymus - do you see where I am going with this? To prove later-no-harm is not applicable to approval requires an argument for how the method's algorithm is categorically different in such a way that the preference criterion does not apply, and can not rest only upon a semantic interpretation of the word "preference".

Thanks to any contributors for comments/suggestionsFilingpro (talk) 10:29, 14 April 2012 (UTC)

It is a little bit confusing to discuss this one issue at two places, so I will answer here to both posts.

(1.) I do not unambiguously agree that Approval violates LNH from a voter’s perspective, but I accept it as part of the compromise position used in the article. I see that mathematically Plurality and Approval satisfy LNH, but in the spirit of the criterion, it is not applicable to them, since there don't exist the possibility to express lower(=later) preferences on the ballot.

(2.) ad "A PROOF THAT APPROVAL MEETS WOODALL’S DEFINITION OF PREFERENCE ELECTION RULE". You totally missed the one (for this discussion) important word in the definition of "election rule". It is the word "profile". That is the only word in the cite that is of interest for this discussion. The definition of profile from your link (Woodall 1994; http://www.votingmatters.org.uk/ISSUE3/P5.HTM, section 2):

"Each voter casts a ballot containing a preference listing of the candidates, which is written as (for example) abc, to denote that the voter places a first, b second and c third, with no fourth choice being expressed. [...] A profile is a set of preference listings, such as might represent the ballots cast in an election."

This is the part, your "proof" would have to deal with. So, how would you express an Approval ballot with a, b approved and c disapproved in Woodalls definition of preference listings?

Either ab or ba, which candidate appears later in the listing is irrelavant.Filingpro (talk) 00:22, 15 April 2012 (UTC)

It may be helpful to point out that Woodall’s explicit requirement of preference ordering in the profile does not contradict the aforementioned proof, rather it is stated a given in the proof and explicitly in the complete proof below. Do you still see a contradiction? (Please see also discussion below) Kindly Filingpro (talk) 00:22, 15 April 2012 (UTC)

But this changes the underlying relation (you added $a>_{s}b$, although $a\not >_{a}b$; analoguos for ba), thus your approach is an encoding. If you want to say something about criterion compliance you need an embedding, not an encoding (see below (9)). --Arno Nymus (talk) 01:02, 15 April 2012 (UTC)

(3.) However, since Woodall concentrated on strict rankings with equal ranks forbidden (see e.g. the beginning of section 6), the generalization of the definition to preference lists with equal rankings (of which approval in fact could be considered a subset with all approved considered equals), is obvious. Since Woodall didn't considered equal rankings, he used the term "any candidate already listed [on the ballot]" for "any candidate for whom a higher preference is already expressed [on the ballot]".

Adding a later preference to a ballot should not help any candidate for whom a higher preference is already expressed [on the ballot]

Still, Approval satisfies that from mathematical perspective.

(4.) ad footnotes: The footnotes are important, since Approval and Plurality satisfy the criterion mathematically. There is no possibility to express a lower preference with Approval or Plurality. Thus, it is not possible, that a candidate is harmed because a voter expressed lower preferences on a ballot. The footnote have to explain why they are not considered satisfying the criterion, although mathematically they do. So, the footnotes should NOT be removed, if there is something different from "YES" in the LNH-columns.

(5.) Homunq's porposal to replace the NA by a blank would be acceptable. --Arno Nymus (talk) 12:15, 14 April 2012 (UTC)

I can't make head or tail of Filingpro's "PROOF". If I wanted to convert a truncated preference order to an approval ballot, the obvious way would be to count all ranked candidates as approved. But that has the ridiculous result that a ballot which ranks all candidates (the maximum information available in a ranked ballot) counts as approving all candidates (a zero-information ballot). Thus if that conversion is the gist of this proof, then I reject its validity. Homunq (talk) 13:25, 14 April 2012 (UTC)

Further deliberations follow re: Homunq and Arno Nymus recent posts. I have also moved my first posting on this talk from the other section to this section above, since this new section on LNH approval focuses on new findings based on the definitions in Woodall's original work Filingpro (talk) 18:03, 14 April 2012 (UTC)

Thank you Homunq and Arno Nymus for your comments and questions. I see this may take some time for us to come to consensus, and in attempt to reach that consensus I do have several follow up questions that may help you articulate your reasoning and by answering your thoughtful questions I can articulate my reasoning. Before that, however, I would like to convey the essence of the issue briefly to see if this is persuasive for you both, so that we may settle the question more quickly:

Woodall’s definition of the profile as a preference ranking that is optionally truncated does not exclude approval from being a member of the class of preferential voting rules. This has been shown by the proof labeled “EXPANDED” above (please see that proof directly above, as this version of the proof may clarify your questions).

Put in other terms, the fact that Woodall is strictly discussing preference order profiles does not exclude approval because approval simply disregards the preference ordering in its computation method. Generating an approval ballot that submits an arbitrary ordering is trivial.

Thank you again for your questions and comments. Rather than respond to each please kindly first let me know if you are not convinced by this simple form of the argument. Thank you for deliberating. Filingpro (talk) 18:03, 14 April 2012 (UTC)

I am not sure I understand it, but insofar as I think I do, I do not accept it. Two-candidate, one-voter election. Vote in Woodall's notation is ab. Who wins in your version of approval? Homunq (talk) 18:28, 14 April 2012 (UTC)

a and b are tied.

Whichever tie resolution method you use for any approval method A1, I can show there exists a mathematically identical method A2 which is a member of the preferential election rules defined by Woodall. (please see further detailed posting below)Filingpro (talk) 22:33, 14 April 2012 (UTC)

Meanwhile, can you respond whether blanking out the NAs (but leaving the same color) would be acceptable? It's hard for me to believe that we're spending an entire section debating between a red "NA" or blank on one hand, and a red "No" on the other. Homunq (talk) 18:51, 14 April 2012 (UTC)

Thanks again for the offer, although I am currently challenging the basis for the conclusion that approval is exempt for the application of later-no-harm. I would like to build consensus on this decision as it is prior to your offer. Re: expediting the decision, you may consent to “NO later-no-harm”, “YES later-no-help” in the table although I would still like to get consensus from Arno Nymus, which I believe requires getting buy in from Arno Nymus that the argument for exemption of approval from preferential election rules is a semantic interpretation rather than a mathematical (i.e.algorithmic) proof.

I propose we keep in mind that Approval voting is said to have been invented (i.e. proposed) in 1968. The attribution of later-no-harm to the method may remain in the body of social choice theory for known human existence. Ascertaining its correct mathematical relationship to later-no-harm criterion is a highly critical question, and one of enormous responsibility.Filingpro (talk) 22:33, 14 April 2012 (UTC)

Homunq - in addition to the discussion below, please also see specific indented responses to questions immediately above - Thanks, FilingPro

Re: Homunq's point: “If I wanted to convert a truncated preference order to an approval ballot, the obvious way would be to count all ranked candidates as approved”. Yes. Are you agreeing that the expression of approval voting as a preferential voting rule is trivial? Filingpro (talk) 22:33, 14 April 2012 (UTC)

Re: Homunq's point: “But that has the ridiculous result that a ballot which ranks all candidates (the maximum information available in a ranked ballot) counts as approving all candidates (a zero-information ballot)” YES. Failing later-no-harm can be viewed as ridiculous, especially when maximally violated as is with approval. The method you are commenting on is mathematically identical to approval. Are you agreeing that approval violates later-no-harm, in a ridiculous way, in fact? Kindly, Filingpro (talk) 22:33, 14 April 2012 (UTC)

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COMPLETE PROOF THAT LATER-NO-HARM NECESSARILY APPLIES TO APPROVAL

Let A1 be an approval method defined as follows:

Method A1: For any set of optionally truncated listings of approved candidates “abc…etc” in any order, perform an approval count.

Secondly, based upon Woodalls’ definition of preference election rules requiring strict preference ordering of candidates which are optionally truncated:

Let election rule A2, a member of the class of preference election rules, be defined as follows:

Method A2: Create a ballot in which a voter may either mark or not mark each candidate on said ballot having a fixed, predetermined preference ordering of candidates (in arbitrary order). Perform an approval count on the resulting optionally truncated orderings.

Method A1 and method A2 are mathematically equivalent because for any input X of profiles, each method returns the same output Y. We know this because the ordering of the candidates in the profile is irrelevant for approval, while all that is required is for a voter to optionally truncate the listing.

Because A1 is approval voting and A2 is mathematically identical to A1, therefore A2 must also be approval voting. We can show for any approval voting system A1 there exists a method A2 which is mathematically identical and meets the definition of a preferential election rule, using the same strategy.

Because A2 is a member of the class of preferential election rules as defined by Woodall, A1 is also a member. If A1 is a member of preferential election rules then later-no-harm criterion applies.

END PROOF Filingpro (talk) 22:33, 14 April 2012 (UTC)

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Please see also individual answers to Arno Nymus deliberation questions above, in the prior post, indented.

Re: Arno Nymus recent post: May I ask, is the current mathematical proof persuasive? Do you have any questions? Would you like an individual response to the assertions in your recent post? Thanks for your cooperation.Filingpro (talk) 22:33, 14 April 2012 (UTC)

Explanation provided with due consideration to Arno Nymus: For any mathematical definition of approval provided, it can be shown another definition of a mathematically identical approval method exists which is a subset of preference, under Woodall’s definition of preference election rules. Therefore the semantic interpretation of “preference” that explicitly excludes “approval” has no mathematical basis under the conditions set by Woodall. Filingpro (talk) 00:22, 15 April 2012 (UTC)

First of all: I don't consider the issue whether Approval could be interpreted as a strict (i.e. no equal ranks allowed) ranking method as the crux of the matter. For my point of view, the intuitive meaning of "later preferences" is the reason, why I don't agree with a "no" (see (3.) above). This is adressed in the points (6), (7), (8). The points after that answer additional questions (mainly about the "proofs").

(6) Woodalls definition of LNH begins with "Adding a later preference to a ballot should [...]". I understand that this means that the prerequisite for a failure to LNH is that some voters have to explicitly express a lower preference on a ballot. That is not possible with Approval. Thus, mathematically Approval can't fail LNH. Obviously, the reason for that is that Approval underlies the more important (than LNH) drawback of not allowing later preferences.

(7) Approval only allows equal ranks that could harm candidates of the same rank. So, Approval does not satisfy "equal-no-harm" (ENH), but that is a different (and somehow silly) criterion. Ignoring that this is a different requirement, would also bring up the question how equal ranks (for methods on rankings with equal ranks) would be treated in regard of LNH.

Consider for example the method "LPE: Least Popular Elimination (with equal ranks)" (the intuitive generalization of IRV to rankings with equal ranks), which I define in the following way:

• Each ballot is a ranking with equal ranks allowed
• As long as there are no equal ranks, the method is exactly IRV
• If one voter has more than one (not-eliminated) candidate on his active rank (say n equal candidates), his vote is split up to these equal candidates (each candidate has ${\frac {1}{n}}$ votes from that voter). If one of these candidates is eliminated, the other equals would have ${\frac {1}{n-1}}$ votes of that voter. Only if all equal candidates are removed, the vote is transferred to the next rank.
• e.g.: one voter has the preference order A > B = C = D > E

First A has a full vote. Assume A is eliminated, than B, C and D has each ${\frac {1}{3}}$ of a vote. Assume C is eliminated. Now, B and D has ${\frac {1}{2}}$ of a vote. Assume, D is eliminated. Now, B has one vote. Assume, B is eliminated. Now, E has one vote.

This system satisfies LNH, since e.g. the later preference E cannot harm B, C, D, A; also the later preferences B, C and D cannot harm A. This system fails ENH. Please say, whether you agree with these two facts (LPE satisfies LNH; LPE fails ENH).

(8) So, as stated above (3.), in compliance with Woodalls definition for methods with strict rankings, the definition for methods with equal rankings allowed is

Adding a lower preference to a ballot should not help any candidate for whom a higher preference is already on the ballot

In fact, this is Woodalls definition with the latter part formulated more clearly. Please state whether you agree.

I believe point 8 is a result of a set of arguments starting back at point 7, specifically regarding equal rankings.

The first supposition “Approval only allows equal ranks” from 7 above is not always true because an approval method can accept preferential ranks and simply ignore the preferences. Consider as an example hybrid methods such as ICA (Improved Condorcet Approval). Also as I have shown any approval method can be expressed as a preference method satisfying Woodall’s criteria (further deliberation on the proofs below).

I) Since LNH explicitly demands the expression of a later preference on the ballot (see (6)), "hidden" preference orderings in the heads of the voters are not relevant for this criterion (note, that e.g. the Condorcet criterion do not demand to have the preferences expressed on the ballot).

II) Just no. You didn't show that. Your "proof" is wrong and I explained why it is wrong (see (9)). So, if you just ignore that and continue to claim you've proofen that, this destroys the basis for a meaningful discussion. --Arno Nymus (talk) 16:44, 15 April 2012 (UTC)

I agree with your assessment that equal-no-harm is different than later-no-harm and is essentially a useless criterion because a superior criteria would better distinguish various voting methods rather than fail to distinguish. Note that under your interpretation of later-no-harm, the criterion fails to distinguish approval for which “a b” nullify each other relative to the race between the two which is the maximal harm that a second choice can accomplish, as opposed to an unequivocally exempt method, plurality for which a second choice is impossible and the criterion is justifiably not applicable in every case. Thus the editorial interpretation is one that unquestionably weakens the criteria, regardless of the justification given.

No, it does not weaken the criterion. For strict rankings this formulation is unambiguously functionally exact the same as Woodalls. (and Woodalls definition is for strict rankings). Thus, this does not weaken the criteria, but is exactly the same.

In my interpretation this formulation is also for not-strict rankings exactly the same as Woodalls definition, but it is formulated more clearly. In your interpretation it differs for not-strict rankings. So, my clear formulation shows how I understand Woodalls definition. Feel free to add a clear formulation of your interpretation of the criterion. I suggest, that you first answer the questions I asked you at the end of (7). --Arno Nymus (talk) 16:44, 15 April 2012 (UTC)

Having said that I do not want to stand in the way of you making your broader point and I would like to cooperate with any hypothetical questions you ask. Are you offering a modification of Woodall’s Later-no-help that works for equal rankings? My cursory look at your logic looks quite sound but I am confused as to how later-no-help for equal rankings is relevant, but please clarify if I am missing an important point you are attempting to convey.Filingpro (talk) 15:37, 15 April 2012 (UTC)

I'm offering a clearer formulation not a modification of Woodalls's Later-no-help. This handles equal ranks. Since approval is easily embedded (without changing semantics) as a not-strict preferential voting method, this solves the problem. --Arno Nymus (talk) 16:44, 15 April 2012 (UTC)

(9) I object to the "expanded proof". If I understand it correctly, you show that every Approval ballot can be encoded in a truncated ranking (ballot) by using the truncation as the approval threshold. This encoding however changes most of the semantics. In fact, you change the relation >_a of the approval ballot into a strict rankings relation >_s with addition of an arbitrary ranking of all candidates that are approved (i.e. for the set of all approved $A:=\{c|\exists d:c>_{a}d\}$ the following change property holds: $\forall a,b\in A:(a=_{a}b\wedge a\not =_{s}b)$ with the obvious meaning of $=_{\cdot }$ derived from $>_{\cdot }$). However, if you encode information of the ballots, you would also have to adapt the criterion to the changes of the encoding.

Easy example to understand this: Consider Plurality voting. Plurality voting satisfies the Majority criterion.

However, I can encode Plurality voting ballots into truncated ballots by arbitrarly rank all the other candidates and let the plurality ballot candidate be the only candidate behind the truncation. (plurality ballot "a" is encoded as 4-candidate strict ranking "bcd").

The strict preferential method PV2 gives every candidate that is ranked no points and every unranked candidate one point. The candidate with most points is the winner.

Obviously, for the encoded plurality ballots, PV2 is functional identical to Plurality voting on the not-encoded ballots.

Also, obviously, PV2 fails the Majority criterion. Does this mean, that Plurality fails the Majority criterion? Obviously not. Instead this means, that I missed to adjust the Majority criterion to the encoding I did on the ballots.

Thus, I object to your "expanded proof", because whether a method on encoded ballots satisfies or fails any criterion, does not say anything about a method that elects the same winners on the not-encoded ballots. --Arno Nymus (talk) 00:39, 15 April 2012 (UTC)

Thank you for responding. I would like to propose an agenda for myself in responding that I intend to help us focus and advance the discussion, and so I have a few questions first:

Q: Firstly, am I understanding your overall position correctly? (1) You have a structural objection to the proof that leads to a contradiction (2) Later preferences are not possible in approval therefore later-no-harm does not apply, only equal-no-harm

Because the proof is a new angle not brought to bear in the previous discussion section, I will begin by focusing on that - i.e. #1; however, that is not to either disregard or concede to your position #2 to which we can debate its validity, if necessary.

RE: the proof objection. I notice you are encoding a plurality ballot vote for "a" in a four-candidate election as "bcd" (I would have expected you to simply encode "a" which is a truncated listing in a four-candidate race). This leads me to ask if I might not have explained clearly my encoding method. I would like to make sure we are on the same page here first. To be clear, I am posting here Woodall's definition of truncation:

"Each voter casts a ballot containing a preference listing of the candidates, which is written as (for example) abc, to denote that the voter places a first, b second and c third, with no fourth choice being expressed. A preference listing is complete if all candidates are included in it and truncated if some are left out."

So, for example, an approval for only "a" in a four candidate race would be expressed as only "a" which is a truncated ballot. An approval for "a" and "c" could be either "ac" or "ca".

Q: Is this the definition of truncation you are using and have understood to be used by my proof?

Q: If not, because you are the subject matter expert of your rebuttal to the proof, is there anything that needs to be updated or is your rebuttal still relevant, before I respond?

Please disregard the cancelled text. I understand in your rebuttal to the proof that the inverse truncation method of the encoding is deliberate, and in my opinion very clever. I will show in another posting how the proof that approval is a member of the preference election class still holds etc... In the meantime, thank you for this mindful rebuttal.

Thanks for your cooperation.Filingpro (talk) 04:40, 15 April 2012 (UTC)

In a two-candidate election, using Woodall's definitions, the vote a is strictly equivalent to the vote ab. (And in general for n candidates a vote of length n has an equivalent vote of length n-1.) When you change this to an approval ballot, this is no longer the case. Thus, the conversion process is not valid, as it does not preserve the mathematical structure of the set of possible ballots.

And anyway: please, no more proofs. Even if the proof were valid, it would be WP:OR. Let's talk about the words on the page. NA, blank, or No? I say, either of the first two is fine. Homunq (talk) 11:27, 15 April 2012 (UTC)

Please also see responses within Arno Nymus last post by Filingpro

Clarification question for Arno Nymus: Imagine months ago (i.e. before the current deliberation) you were told about a new voting method PV2 (exactly as you defined it above). Now imagine you were tasked as an editor determine what to write for PV2 under the compliance chart column for Majority criterion. What definition of Majority would you apply and what would your answer be?Filingpro (talk) 15:37, 15 April 2012 (UTC)

If there would be no claim that this method shall be used for encoded plurality ballots, I would use the normal Majority criterion and the answer would be "FAIL". Obviously, this would say nothing about Plurality voting. So, what's your point about that? --Arno Nymus (talk) 16:44, 15 April 2012 (UTC)

@Homunq: I agree, with "NA, blank, or No? I say, either of the first two is fine."

@Filingpro: What's your answer to Homunq's question?

I replied to your responses within my post above and the clarification question. --Arno Nymus (talk) 16:44, 15 April 2012 (UTC)

Homunq asserts in prior post: "In a two-candidate election, using Woodall's definitions, the vote a is strictly equivalent to the vote ab", however,

Woodall states "A preference listing that leaves out just one candidate will be treated by most election rules... as if it were complete; but one should not call it complete, since some election rules may not treat it as such. Do you agree that your assertion is false and therefore there is no basis for the argument you proposed?Filingpro (talk) 15:52, 15 April 2012 (UTC)

Homunq asserts in prior post: Even if the proof were valid, it would be WP:OR

No original research rule applies to articles, not talk pages. Proofs are synonymous with logical reasoning and argumentation for the editorial decisions in question. If you prefer I can refer to the condensed form arguments as SUMMARY OF ARGUMENT. Which term would you prefer for argument summaries on the talk page?

Re: words on the page "NO" because I have not YET been persuaded that LNH can not be applied to approval. Further argumentation may change my assessment.Filingpro (talk) 16:09, 15 April 2012 (UTC)

re: Arno Nymus recent posts...Yes I was waiting for your clarification response to continue deliberation re the proof. You have demonstrated an interesting contradiction that I will respond to. Thanks for your postings and no miscommunications intended...I will review your other comments above as well.Filingpro (talk) 17:20, 15 April 2012 (UTC)

2nd note re: Arno Nymus recent posts. Ahhh I see another miscommunication that can be easily cleared up. Firstly, on my review of your adapting Woodall's definition, I am generally endorsing your clearer formulation not a modification of Woodalls's Later-no-help, kudos - this looks very sound. I was simply pointing out entirely separately that the interpretation of later-no-harm that renders approval not applicable leads to an inferior criterion from the standpoint that a superior criterion would better distinguish various voting methods rather than fail to distinguish them, which I'm sure you would agree. Your position is that we are bound and obligated editorially by certain language in Woodall's definition namely "preference" which in your interpretation demands exclusion of approval, even though the effectiveness of the criteria suffers as a result. I hope we are back on good faith deliberatin terms. Now working on the response to your proof contradiction... Filingpro (talk) 17:39, 15 April 2012 (UTC)

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Response to proof rebuttal/contradiction etc…from Arno Nymus

RESPONDING TO THE "REVERSE ENCODING" PARADOX FOR VOTING CRITERIA

I found fascinating that the contradiction you constructed exists prior to my proof. In other words, imagine my proof never existed. You still described what could be a real-world voting method PV2. As you point out, this method is mathematically identical to Plurality; specifically from the standpoint of any voter input X produces the exact same single winner Y. They are identical, yet as you pointed out it is possible to find at least one criteria (which does not respect the encapsulation of the voting method – I will explain that later*), and therefore returns different (i.e. paradoxical) result.

-We cannot say that PV2 does not exist, because if it does not exist then it also doesn’t exist for my proof and no contradiction to my proof would be shown and the proof would still stand.

-On the other hand, if we acknowledge that PV2 exists, then it must have existed prior to my proof. Before my proof, I could have shown PV2 responds to Majority criteria differently than plurality, which is a failing of the criteria and therefore has nothing to do with my proof.

In other words, your idea of reverse encoding the ballots might have been applied to any voting system to potentially cause certain criteria* appear paradoxical. This fact that the same encoding problems still occur in my proof doesn’t mean I have violated any new voting axioms, it just means my proof lives under the same axioms as the voting world prior.

Note that all I need to do is prove that a criteria applies, it is not my burden to also solve a failing of how certain criteria perform, especially when that failing existed prior.

Therefore I hold my proof still stands, because you have pointed out an interesting contradiction that exists prior and independently, and therefore cannot be a fault with any reasoning in my proof.

• The argument above suffices, but it may be a matter of interest to know the nature of the paradox you discovered, in my current assessment of it:

Note that any criteria that is expressed only terms of voter markings and election results cannot produce a contradiction. This categorically includes the class of criteria which Woodall defines as “local or relative properties” for which later-no-harm is a member. Therefore it is impossible to show this contradiction with later-no-harm, which only further proves that the contradiction does not apply to this discussion. It’s further possible we could show that any criteria which produce the paradox by violating the encapsulation of the voting method can be trivially rewritten only in terms of voter markings and results. This would be a longer exercise and not required for our purposes, but here is an example:

Majority Definition #1 (Pluarlity = FAIL – CONTRADICTION by certain interpretation)

Majority. If more than half the voters put the same set of candidates (not necessarily in the same order) at the top of their preference listings, then at least one of those candidates should be elected.

Majority Definition #2 (Pluarlity = PASS - modified)

Majority. If more than half the voters mark the same set of candidates (not necessarily in the same order) as top preference on their ballots, then at least one of those candidates should be elected.

Note the paradoxical/unexpected failure of definition #1 is the result of the definition making explicit references to preference listings, but only when these are semantically interpreted to mean the encodings rather than the voters ballot markings. Trivially one could consider the preference listing to mean those first indicated by the voter before being encoded – some would argue this is an obvious interpretation. This would also eliminate the paradox.

So one might argue that if any voting criteria can be expressed solely in terms of the ballot marking by the voter and the results, and if voting criteria were mathematically defined as be required to do so then the paradox might not be relevant.

This could be looked into further but as I said is not needed and is not my burden to solve a prior paradox, (if it really exists at all) which also depends on the proper mathematical definition of various criteria or semantic interpretation – again not the responsibility or scope here.

Finally, I claim, because approval voting is mathematically proven a subset of preferential election rules defined by Woodall, later-no-harm applies. Filingpro (talk) 19:40, 15 April 2012 (UTC)

Sorry, but this is terrible. You got nearly everything wrong. I am not sure, if you want to make fun. That can't be serious.

• There is NO paradox. There is only the easy and intuitive fact, that changing the semantics of a voting system will change the compliance with criteria.

Changing the semantics of the voting method is irrelevant when the semantics are fully encapsulated in the method, while the criteria are only concerned with the voter markings (input) and the election result (output), and therefore compliance with said criteria cannot be changed. (see also "Q" & "A" below) Filingpro (talk) 06:17, 16 April 2012 (UTC)

No. Simplified: Let C be the set of candidates, V be the set of voters. Approval is a voting method $AV:({\mathcal {P}}(C)^{|V|})\to C$. But Woodalls definition of LNH is designed for strict ranking methods, which has the form $V:(C^{*})^{|V|}\to C$. Both have characteristic ways to realize the preference relation from a ballot. Your proof have to show, that you have an encoding $enc_{a}:({\mathcal {P}}(C)^{|V|})\to (C^{*})^{|V|}$ and a strict ranking method AV', such that (i) $AV'(enc_{a}(P))=AV(P)$ and (ii) the encoding is semantically invariant, that means, it does not change the relational realization of the ballots.

So, if you say, the encoding is encapsulated within your method, this means, your method has the signature $AV2:({\mathcal {P}}(C)^{|V|})\to C$ and would still NOT be a strict ranking method and therefore, it would be completely useless.

In fact, you are using your method in the way of AV' with $AV'(enc_{a}(P))=AV(P)$. Now, you can say, AV' is a strict ranking method. But, since your encoding enc_a is not semantically invariant, using AV' does not say anything about criteria compliance of AV. --Arno Nymus (talk) 11:09, 16 April 2012 (UTC)

I have studied this thorough response above and is appreciated. I believe to understand it clearly to be address below in the "YES"/"No" argument which you offer and I respond to (below).Filingpro (talk) 20:16, 17 April 2012 (UTC)

• The example of PV2 is just another encoding that illustrate how changing semantics changes compliance to criteria. This example is analogous to your AV2 encoding. But, obviously, there is no direct reasoning between PV2 and AV2. It just is an easy to understand analogon.
• PV2 is NOT functionally identical to Plurality. Instead, PV2 on the encoded plurality ballots is functional identical to Plurality on the not-encoded ballots. That is an important difference. $PV2(enc(P))=PV(P)$, but $PV2\not =PV$.

In my definition of PV2 it does not receive as input the encoded ballots. It receives as input voter markings. Creating the ballots with the encoding is part of the method. For example def A2 in proof "Method A2: Create a ballot in which a voter may either mark or not mark each candidate on said ballot having a fixed, predetermined preference ordering of candidates (in arbitrary order)" Therefore A2 receives the same input as A1 (standard approval) and because they always produce the same result they are functionally equivalent. I hope this helps clarify. Filingpro (talk) 23:47, 15 April 2012 (UTC)

It receives as input voter markings. So, is this the same input as for the other method?

If the answer is...

...YES: the new method operates on the same inputs as normal Approval voting. Obviously, the "new" method is not a strict ranking method, since strict ranking methods have strict rankings ("ordered sets") as input and normal Approval has (not-ordered) sets of candidates as input. The "new" method would be useless.

Thank you I believe we have both argued well here. The problem I see with this rebuttal is that it’s trivial for me to construct a ballot that contains preference listings (to satisfy Woodall) while the voter input is functionally equivalent to approval. Since the voter’s actions can be the only determining factor in changing a profile and since the output is the same, there is no change in compliance with criteria.

It may be, as I believe you also mentioned that we have a fundamentally different conception of voting methods, and criteria and their relationship – i.e. different axioms of voting systems we are operating on. I have offered a new immaculately simple, in my view, solution below that may exempt us from trying to resolve this debate – see “NEW PROPOSAL” (to be added below). Filingpro (talk) 20:16, 17 April 2012 (UTC)

....NO: this means the input to the "new" method is an "encoded" version of the ballots for normal Approval voting. Everything that I wrote above applies, especially that by the fact, that the encoding you use is not semantically invariant, the "new" method cannot be used to say anything about criteria compliance of Approval. --Arno Nymus (talk) 11:09, 16 April 2012 (UTC)

These are only the most important mistakes of the first three lines of your recent comment; to limit the length of my post, I will only reply on one other mistake, although I think, that nearly everything of your comment would have to be corrected:

• The fact that encodings cannot be used for proofing anything about criteria, also holds for LNH. It is easily possible to create a voting method IV2 and a ballot encoding enc_i, so that IV2 fails LNH, but IV2(enc_i) elects the same winner as an LNH-compliant method, e.g.

enc_i: reverse the order of all ranked candidates, the not-ranked candidates stay unranked: abd -> dba

IV2 is IRV with reversed rankings, i.e. start with the last ranked candidate. If he is eliminated, the vote goes to the second to last ranked candidate and so on.

IV2 obviously violates LNH, since it considers the "later preferences" first. Nevertheless, IV2(enc_i(P))=IRV(P). Does this say anything about IRV? No.

Now that I have clarified my definition of "functionally identical" to include the creation of the ballots with the encodings as part of the voting method, then is this counter example, to which you are the subject-matter expert, still relevant? If yes and you would like me to still respond please let me know. Filingpro (talk) 23:56, 15 April 2012 (UTC)

Yes, it's still relevant. --Arno Nymus (talk) 11:09, 16 April 2012 (UTC)

Please use these clues to think again about the issue. --Arno Nymus (talk) 21:11, 15 April 2012 (UTC)

Q: Can you give at least one example directly from the steps of my proof which "changes the semantics", as you say, of approval, and achieves a different compliance with criteria later-no-harm? Thank you.Filingpro (talk) 23:21, 15 April 2012 (UTC)

We have different views on the mathematical compliance (and applicability) of Approval for LNH, so how should I interpret "achieve a different compliance with [LNH]"? Obviously, the preassumptions in the question prevent from giving a meaningful answer. That's like the question "Why is Hubert the best man in the universe?" If Hubert is not the best man in the universe (or you think so), you cannot answer that question.

However, I can easily show you the change of semantics. Assume a three voter election with one voter that approves candidates x and y, but not z.

normal approval: the voters ballot is {x, y}. This induces the relation $>_{a}=\{(x,z),(y,z)\}$

your encoded approval: the voters ballot is x > y. This induces the relation $>_{e}=\{(x,y),(x,z),(y,z)\}$

Obviously, the semantics changed.

Furthermore, for your claim that LNH is failed, you are using $x>_{e}y$ in your assumption that y is a "later preference" to x, although - in fact - it isn't: $x\not >_{a}y$ --Arno Nymus (talk) 11:09, 16 April 2012 (UTC)

I agree with the problem as you pointed out with the question. My apologies. What I had intended is to challenge your assertion “changing the semantics of the voting method changes the compliance with the criteria”. If this were true then approval methods A1 and A2 as explicitly defined in my proof would have to be shown to have different compliance with at least one criterion. What I am arguing is that if you run down the compliance table for approval, e.g. pick say IIA, you can never show that A1 and A2 exhibit different compliance.

As perhaps we have both agreed, we may have different axioms of voting methods and criteria we are operating on, and so I have offered what I believe a very simple solution to our problem within Wikipedia guidelines below – see “NEW PROPOSAL” kindly Filingpro (talk) 20:16, 17 April 2012 (UTC)

A: The reason it is mathematically impossible to find such a counterexample in “Q” above, is that any change in the internal semantics of the method are not relevant to later-no-harm criterion, which, as a local and relative property defined by Woodall, is only concerned with a change in profile caused by a change in voter markings (input) and how this affects probabilities of certain winners (output). Since the proof constructs a functionally identical voting method to approval (i.e. same input leads to same output) it will not be possible to find a case demonstrating a change in the compliance of the criterion.Filingpro (talk) 06:08, 16 April 2012 (UTC)

No, the reason is the unreasonable question. You're question only makes sense if some assumptions are correct, that you want to be, but that aren't in my opinion (see above). --Arno Nymus (talk) 11:09, 16 April 2012 (UTC)

Please see response in 'Q' immediately aboveFilingpro (talk) 20:16, 17 April 2012 (UTC)

Please also see important comment above regarding clarification of definition of "functionally identical" which may be of assistance.Filingpro (talk) 23:47, 15 April 2012 (UTC)

I really don't want to eternally argue proofs here, when we all agree on the color/sort order, which to me is the important thing.

Again, let's try the easy way first. You're making a (totally unciteable) argument that "No" would be true. I disagree but don't think we have to resolve that argument. As a gesture of good will, I've set the cells under discussion to blank. Do you have any reason why that is not acceptable? (You may not think it's optimal, but at a certain point compromise is the only way to stop arguing.) Homunq (talk) 01:12, 16 April 2012 (UTC)

Thank you for your sincere effort to compromise and I do prefer only as a temporary marking the blank designation. Thank you for that gesture of good will which is much appreciated. Meanwhile, I also see no evidence that enormous progress has not been made in our deliberations to potentially lead to a successful consensus.

With the proof that approval is a mathematical subset of Woodall’s preference election rules, we now have a prima facie case that later-no-harm can be applied to approval, only further evidenced by the plain language in the definition of the word approval “applying or capable of being applied; relevant; suitable; appropriate: an applicable rule; a solution that is applicable to the problem.” http://dictionary.reference.com/browse/applicable

Note also that the term “harm” is clearly defined by Woodall before he uses the word elsewhere. Woodall states, “Local or relative properties [to which later-no-harm is a member] are concerned with what happens when a profile is changed in some way. We shall say that a candidate is helped or harmed by a change in the profile if the result is, respectively, to increase or to decrease the probability of that candidate being elected.” In approval the change from “a” to “a b”, by adding b later in the listing, decreases the probability of “a” being elected. Therefore there can be no editorial interpretation under which the addition of a later listed candidate can not cause harm for approval voting.

The designation “non-applicable” would require a very high standard of justification which has not been provided, and to which only one counterexample is needed to disprove. Meanwhile it has been proven later-no-harm is applicable to approval in all cases.

Therefore I maintain the correct designation "No", indicating approval fails later-no-harm.

I invite contributors to concur. Filingpro (talk) 06:08, 16 April 2012 (UTC)

In fact, your "proof" has been disrupted. Apart from that, I don't see that this discussion progresses.

Although the correct entry for the cell would be "NA" or "Yes", in favour of compromise, I am ok with a blanked out cell. --Arno Nymus (talk) 11:09, 16 April 2012 (UTC)

Enormous progress has not been made. Your "proof" is not germane to the page, because it is WP:OR.

(Although this is irrelevant, it also rests on an equivalence that I dispute. I acknowledge that Woodall allowed for the possibility that in (say) a 5-candidate election, an abcd vote would not be precisely equivalent to an abcde one. But he never allowed that the latter would be equivalent to a ∅ one or an edcba one. The ridiculousness of this is most evident in the two-candidate, one-voter election example I gave.)

• Woodall does allow 'abcde' to be treated as 'edcba' by a preference election rule. There is nothing in Woodall's definition of a preference election rule that prevents a method from computing an election result such that 'abcde' and 'edcba' are treated the same. Please provide evidence from Woodall's definition to support your claim.
• You refer to the case of a 5-candidate election whereby a voter marking 'abcde' (marking every candidate) being equivalent to a ∅, as "ridiculous". This is the precise functioning of approval voting which you are referring to. This is only further evidence that, in the proof, approval voting is flawlessly and trivially expressed as a preference election rule, and therefore later-no-harm applies to approval.

No, it's not. Approval does not handle "a > b > c > d > e" as ∅. It does not handle it at all, since it is not a strict ranking method. --Arno Nymus (talk) 04:06, 17 April 2012 (UTC)

In my proof, both functionally identical methods A1 and A2 treat a voter approving all 5 candidates "abcde" the same and compute the correct election result.Filingpro (talk) 19:57, 17 April 2012 (UTC)

• re: "the two-candidate, one-voter election example" you gave, you claim that according to Woodall's preference election rules "the vote 'a' is strictly equivalent to the vote 'ab' which is an incorrect assertion. Woodall explicitly states, "A preference listing that leaves out just one candidate will be treated by most election rules... as if it were complete; but one should not call it complete, since some election rules may not treat it as such."

Filingpro (talk) 20:27, 16 April 2012 (UTC)

Since you have given no reasoning for the blank cells to be considered unacceptable (as opposed to simply suboptimal) from your perspective, I personally consider this issue resolved as of now. Even if you convinced me that your proof was correct, that would still be my position, because it would still be WP:OR; so please don't try. Homunq (talk) 12:02, 16 April 2012 (UTC)

re Filingpro's list of res:

For every of these statements, there is a lot of basis/argumentation in my explanations above. --Arno Nymus (talk) 04:06, 17 April 2012 (UTC)

Thank you - I shall respond directly above.Filingpro (talk) 19:50, 17 April 2012 (UTC)

re: Arno Nymus assertion, "In fact, your "proof" has been disrupted."

This assertion has no basis. Please provide argumentation or basis for this assertion. Thank you Filingpro (talk) 19:35, 16 April 2012 (UTC)

In fact, this assertion has a complete logical basis above. Also, at my last post (from 11:09, 16 April 2012 (UTC)) I added replies to clarify some points above. These replies also have additional information on that issue. --Arno Nymus (talk) 04:06, 17 April 2012 (UTC)

re: Arno Nymus assertion, "I don't see that this discussion progresses."

This assertion has no basis. Please provide argumentation or basis for this assertion. Thank you Filingpro (talk) 19:35, 16 April 2012 (UTC)

All participants seemingly now have the same opinion as before. Arguments are interchanged, but merely taken by the others. For example, I disputed your "proof" with clear logical arguments, but you still just claim that your disputed "proof" is a "prima facie" fact. Even if you don't agree with my objections, you should realize that it cannot be "prima facie" at all, since all participations (except yourself) object its validity. That obviously is not a progress. --Arno Nymus (talk) 04:06, 17 April 2012 (UTC)

Thank you for clarifying. I do not claim (or did not intend to) claim my proof is prima facie, but if the proof is correct (i.e. not dis-proven) then we would have a prima facie case for applicability. So we both agree proof is not prima facie. I will offer a new proposal below to help advance our discussion in a different, positive way (to be added below). Filingpro (talk) 19:42, 17 April 2012 (UTC)

re: Arno Nymus assertion, "the correct entry for the cell would be "NA" or "Yes"

This assertion has no basis. Please provide argumentation or basis for this assertion. Thank you Filingpro (talk) 19:35, 16 April 2012 (UTC)

Just see above. --Arno Nymus (talk) 04:06, 17 April 2012 (UTC)

re: Arno Nymus statement, "I am ok with a blanked out cell".

This statement is irrelevant because I am challenging the basis of the designation NA or blank to which you are logically obligated to argue and deliberate prior, while your statement incorrectly presupposes the outcome of this debate to which I have not consent.Filingpro (talk) 19:35, 16 April 2012 (UTC)

Your opinion is not the only one that counts. So, my statement is very relevant. Also, please look at your own posts, where you state your opinion as if it were facts, so don't try to forbid others even to clarify what solution would be ok in their view. --Arno Nymus (talk) 04:06, 17 April 2012 (UTC)

However, many of your stated thoughts have no basis. However, as Homunq explained, your so called "proofs" are disputed and obviously are not "prima facie", so please stop purporting that. --Arno Nymus (talk) 04:06, 17 April 2012 (UTC)

My apologies, I was only trying to be sure that my request for continued deliberation was respected before calling for a vote to which I was not ready to consent to, while remaining open to persuasion. No Malice intended and thank you for clarifying your opinion.Filingpro (talk) 19:35, 17 April 2012 (UTC)

To all contributors I kindly request you submit further argumentation or concur so that we may reach consensus. Rebuttals to Homunq recent posts will follow. Thank you Filingpro (talk) 19:35, 16 April 2012 (UTC)

re: Homunq's assertion "Enormous progress has not been made".

This assertion has no basis. Please provide argumentation or basis for this assertion. Thank you. Filingpro (talk) 19:50, 16 April 2012 (UTC)

re: Homunq's assertion "Your 'proof' is not germane to the page, because it is WP:OR"

Wikipedia Original Research pertains to the article contents, not the talk page contents. It is an axiom of the talk page that argumentation be provided (in the talk page only), as to the editorial decisions in the final article. Please kindly respond to this rebuttal before repeating the assertion without basis. Further rebuttals will follow. Filingpro (talk) 19:50, 16 April 2012 (UTC)

This is tiresome.

A blank cell in red needs no citation. A "No" cannot be based on a proof on a talk page. In any case, a reasonable person will see a red, blank cell and assume it means some form of "no". Which is true, because if we could fit it, we could put something like "effectively, no."

The answer "No" in the cell is based on the best source currently cited which is Douglas Woodall. The talk page does in fact give license to make reasonable argumentation as to the source's contents. Because approval can be functionally expressed as a preference method in a trivial manner, we have a prima facie case, and thus there is no ambiguity unless some other reliable source can be identified which contradicts the determination. Please see further comments below also relating to this issue. Filingpro (talk) 21:24, 16 April 2012 (UTC)

What do you have to gain by continuing this argument?

Thank you for asking. I believe the relevant question is the correctness of the determination and its historical, mathematical, and practical importance to social choice theory which is critical, in my view, and therefore the responsibility of the determination of applicability of later-no-harm to approval is enormous, as I have expressed previously.Filingpro (talk) 21:24, 16 April 2012 (UTC)

Whatever it is, if you're determined to continue, pretend I'm too stupid to understand your proofs, and that I need citations from WP:RS. Homunq (talk) 20:24, 16 April 2012 (UTC)

Certainly. The reliable source is Woodall's document. The discussion on the talk page is regarding the contents of the document and whether the criteria later-no-harm is applicable to approval based on said original source. May I suggest, if you do not want to further participate in the discussion, you might identify a second reliable published source which makes a determination of later-no-harms application to approval, and then you could argue a case for using that determination, even if it was incorrect (i.e. disproven mathematically by my proof).

ps. I think that Arno Nymus meant "disputed", not "disrupted". His English is excellent but it's not his first language. Homunq (talk) 20:26, 16 April 2012 (UTC)

Thank you for clarifying. Everyone's intentions I believe are good here. Filingpro (talk) 21:24, 16 April 2012 (UTC)

Also, while I stand fully by my prior responses, I very much appreciate your sincere effort to offer what you consider as a good faith compromise. Thank you for that gesture. Filingpro (talk) 21:37, 16 April 2012 (UTC)

Also a thank you to Arno Nymus because I see you are continuing to contribute to the discussion by making specific rebuttals in the comments above. I will respond to these thoughtful rebuttals with the intent that we may collectively reach a better consensus. I will keep an open mind to new persuasion and I respectfully ask that all contributors do likewise. Kindly Filingpro (talk) 21:54, 16 April 2012 (UTC)

1. Generally, I prefer it if you leave my comments intact, rather than interspersing your replies. For your convenience, I'm numbering my paragraphs.
2. You say that your proof is based on Douglas Woodall's paper. I presume that your argument is that it is a straightforward calculation covered under WP:CALC. But as you've seen, this is not the case. You may be able to convince the two of us that you are right, but I can already say that when I initially saw your proof, I was not convinced of its validity (and in fact I'm still not.) That demonstrates that this is not a simple, uncontroversial calculation. That's what I was saying by, "pretend I'm too stupid to understand a proof"; anything that demands intelligence and judgment is WP:SYNTH, not WP:CALC, so it may be best for this discussion if you pretend I have neither.
3. Consider your stated reason for pressing this point: "Thank you for asking. I believe the relevant question is the correctness of the determination and its historical, mathematical, and practical importance to social choice theory which is critical, in my view, and therefore the responsibility of the determination of applicability of later-no-harm to approval is enormous, as I have expressed previously." I definitely sympathize with the importance of this topic; if I didn't, I wouldn't be here. But this is exactly the wrong reason to be pressing this particular point. If you consider this to be a matter of historical, mathematical, and practical importance, it is not Wikipedia's role to be the first to express it explicitly.
4. A blank cell can be filled in later if you find an unbiased or peer-reviewed source that explicitly relates approval and LNH.
5. Homunq (talk) 00:12, 17 April 2012 (UTC)

I added some comments above. --Arno Nymus (talk) 04:06, 17 April 2012 (UTC)

note: Though it may seem that Arno Nymus and I are coordinating our arguments here, this is not the case. We know each other only from and on Wikipedia, and as far as I know we each live in (non-English-speaking) countries on different continents. Homunq (talk) 11:40, 17 April 2012 (UTC)

Thank you and I trust both of you have best interests in mind. Diversity is welcomed in my view. I appreciate the cordial tone of recent replies.Filingpro (talk) 20:36, 17 April 2012 (UTC)