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I think the site would benefit from a hierarchical structure to the duplicate question functionality, indicating which questions generalise others.

I was contemplating duplicate questions last night in the context of some of the problems with this site. Thinking it through, many of the problems surrounding deletion of homework / psq's arise from limitations in the duplicate question functionality.

This is because maths is a relatively unique case among Stack Exchange in that as a general rule, maths questions and answers generalise other maths questions and answers.

Then long-time users and better mathematicians easily see that the site is, over time, deluged with a vast array of different questions which are simply new examples of the same thing. To the asker, the new question is not on the site, but a more experienced mathematician instantly recognises it as a new special case of something seen many times before.

If we had a hierarchical duplicate question functionality which indicated whether some duplicate generalised, or was generalised by, another question, it would be possible to navigate a hierarchy of generalisations. This would actually be a powerful learning tool enabling users to learn much more than simply the answer to their question.

A user could not only navigate to a generalisation of their question, but would also be able to navigate among other examples of the same thing.

For example: the OP says "How many distinct ways are there to arrange the letters in the word permutation?"... plus appropriate context etc., and makes it a great question (great for a mathematician of that level - obviously this will never be great for a professor of combinatorics). Then this is easily answered by somebody helpful, but also marked as a duplicate of similar great questions involving permutations of other 11-letter words with 2 duplicate letters. But all of these are identified as duplicates of the best generalising duplicate which covers permutations of $n$ elements with $k$ duplicates.

Then the question says:

this question is a duplicate of , and

this question is generalised by...

It would be easy and natural then, to give the generalisations of questions greater prominence in the site, and subsequent users can quickly use the fabulous duplicate question functionality to navigate to the question with the appropriate degree of generalisation for their needs.

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    $\begingroup$ That's really a big issue! I also think that we should find a way to deal with dulicates other than making battles and war on hinting/answering (one party) and deleting them (the other party). It's really not productive for anyone. The first issue is to help/force the askers to look for duplicates before they proceed to formulate a question. Once the question is formulated I think we need to deal with that in a more effective way. $\endgroup$ – gimusi Dec 10 '18 at 14:45
  • $\begingroup$ From here we can discuss what could be the best way to follow, but at the end in most of the cases we have new duplicates answered to deal with. I think that when a question is well posed and the given aswers are good, we should mantain the duplicates among the repository of MSE and your proposal could be, in principle, a good idea to keep the material ordered and "to build a library of detailed answers". $\endgroup$ – gimusi Dec 10 '18 at 14:57
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    $\begingroup$ In any case, the main/first question should be always linked as reference in the others subsequent duplicates. When a duplicates have a very different new good answer it should be considered at the same level of the first one. In general I would avoid merging duplicates toghether. $\endgroup$ – gimusi Dec 10 '18 at 15:10
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    $\begingroup$ Who gets to decide the hierarchy? Which questions more general than specific? Who do you expect to spend the time creating the hierarchy? (And it shouldn't be a task only one or two users take on.) More details please, as how to implement your idea. (Ideas are the easy part; how to implement or realize them is the harder part.) $\endgroup$ – Namaste Dec 10 '18 at 17:43
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    $\begingroup$ @amWhy same as now, the person who marks the duplicate as a target identifies it. Except when selecting duplicate there would also be a tick box "target generalises the duplicate". $\endgroup$ – user334732 Dec 10 '18 at 19:02
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    $\begingroup$ That doesn't address the current web of duplicates and duplicated answers already linked. Who goes back to decide which are "more generalized" and which "more specific"? $\endgroup$ – Namaste Dec 10 '18 at 19:14
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    $\begingroup$ @amWhy any user can do so, including any group of users who may want to organise themselves into a group and create a room and organise their efforts to kindly improve the repository of answers. $\endgroup$ – user334732 Dec 10 '18 at 19:28
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    $\begingroup$ @amWhy our conversations never seem to end well. $\endgroup$ – user334732 Dec 10 '18 at 23:28
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    $\begingroup$ @user334732 I'm just saying, your request/suggestion will require many "person hours" to enact, and many person hours to maintain. Since you're the advocate here, the proposer, I'm simply asking if you are willing to devote time, and organize a group, to undertake the work your proposal will entail? $\endgroup$ – Namaste Dec 10 '18 at 23:33
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    $\begingroup$ @amWhy I was simply describing something which already exists, as proof positive that such a thing can exist. But I guess that went over your head. $\endgroup$ – user334732 Dec 10 '18 at 23:38
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    $\begingroup$ @user334732 Likely I'm way over your head. A web of links exists for duplicates. No "hierarchy" as you are calling for, exists. I'm simply asking if you are willing to spearhead the organization of an interested and committed group of users who undertake the designation of top-tier, lower-tier, bottom-tier duplicates related through links. If you are happy with the currently existing system which exists, why the question? $\endgroup$ – Namaste Dec 10 '18 at 23:48
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    $\begingroup$ @amWhy a group of users who may want to organise themselves into a group and create a room and organise their efforts to kindly improve the repository of answers. already exists. $\endgroup$ – user334732 Dec 11 '18 at 5:38
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    $\begingroup$ @amWhy I would probably join in the work from time to time like I do now with other tasks. But there would be less of the other stuff to do, because with better signposting of the good stuff there would be fewer duplicate questions and they would pose less of an impediment to using the repository of content, so those currently doing that admin might find they have time for more productive activities such as improving the stock of answers old questions. $\endgroup$ – user334732 Dec 12 '18 at 2:59
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    $\begingroup$ Thank you for your response, @user334732. $\endgroup$ – Namaste Dec 12 '18 at 11:01
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    $\begingroup$ I am reminded of Bill Thurston's wonderful essay "On Proof and Progress in Mathematics" (arxiv.org/abs/math/9404236) where, right near the beginning, he explores the notion of a derivative, and exposes a complex hierarchy of understandings. $\endgroup$ – Mark Bennet Dec 15 '18 at 19:47
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YES YES YES. There's also the question of where to find the good answers to a duplicate question—the best answers aren't necessarily on the best version of the question, and the most general answer might not be on the most general version of the question.

In fact I think the most complete answers are likely to be on the more confused versions, because the questioners need more help in understanding the basic principles needed and how to apply them.

I'd like an easy way to see all the answered duplicates of a question without having to follow This is a duplicate of links or work out what search might bring them up: something like a Possible duplicates of this question link.

A possible default ranking system might be to sort the duplicates by the total number of upvotes on their answers (or maybe the mean), followed by some way for human intervention to adjust it via a "well answered question" score.

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    $\begingroup$ I agree that in general the best answer is not on the best version of the question and this is a problem to me: I usually have to search using different keywords to find the answer which suit me most. $\endgroup$ – Alex Vong Dec 12 '18 at 21:44
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    $\begingroup$ Possible solution: Taking inspiration from bug tracking system, should we provide option to merge questions? Suppose we have duplicated question $Q_1, Q_2$ with set of answers $\mathscr{A}_1, \mathscr{A}_2$ respectively. Then we can merge them to create a new question as followed: the answers would be $\mathscr{A}_1 \cup \mathscr{A}_2$ (This is good, it means good answers from both question would be on the top), while the question field will consist of a single question only, but with a button to rotate between different versions of the same question (the default being the most upvoted one). $\endgroup$ – Alex Vong Dec 12 '18 at 21:57
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    $\begingroup$ @AlexVong That sounds quite nice, but: how does it treat answers which are tailored to particular questioners? "You said you're confused about $A$ but you obviously understand $B$ so I'll explain it this way . . . " It would have to display different sets of answers too, so theyre not fully merged. $\endgroup$ – timtfj Dec 12 '18 at 22:04
  • $\begingroup$ Hmm... Maybe we can provide a "see original question" button for each (merged) answers? $\endgroup$ – Alex Vong Dec 12 '18 at 22:17
  • $\begingroup$ That would do it. I think the answers might need some visual indication of which belong to the currently displayed version of the question as well. $\endgroup$ – timtfj Dec 12 '18 at 22:28
  • $\begingroup$ Agree, a crude way would be to label them with the same number. $\endgroup$ – Alex Vong Dec 12 '18 at 22:30
  • $\begingroup$ I was thinking of a lightly shaded border or something. When you select a question version, it changes and you can instantly see which answers belong to that question. $\endgroup$ – timtfj Dec 12 '18 at 22:33
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    $\begingroup$ @AlexVong, there is already an option to merge questions which is available to moderators, although it doesn't preserve both questions. $\endgroup$ – Peter Taylor Dec 13 '18 at 9:01
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Not every question with duplicate mathematical content is, in fact, a duplicate question. "Help me to understand this step of the proof" or "I'm confused about this definition and how it applies" are quite common in one form or another.

The best answer for one person dealing with the mathematical content might be short and abstract. Someone else might need more detail, or examples, to understand what is going on.

However - I hugely agree that pointing to generalisations, and helping people to put the mathematical material with which they are grappling in a useful wider context, is really important. Curating that on the site is a formidable task, but one which could do with some thought - what tools would make it easier for those minded to make such links to do it in a straightforward and helpful way?

This question is an interesting starter.

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    $\begingroup$ Agreed. One thing I was mindful of when asking this is that the tags organise the hierarchy of generalisations already, but they have nowhere near enough resolution to be useful for this purpose. $\endgroup$ – user334732 Dec 15 '18 at 19:30
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    $\begingroup$ Disagree, because this depends on what the goal of the site is. If the goal is to build a repository of knowledge, all duplicates are basically entropy increasing noise. If the goal is to teach all and sundry askers, then this can be justified. Because a compromise is necessary, we need a more refined policy. A problem with the inclusionist view is the answerers. Currently they use the current strict definition of "duplicate" as a license to duplicate earlier answers. This is particularly visible in proof-verification and solution-verification tags. $\endgroup$ – Jyrki Lahtonen Dec 16 '18 at 10:28
  • $\begingroup$ (cont'd) where the answers prove that the question was, in fact, a dupe even though technically it would not be according to the current practice. $\endgroup$ – Jyrki Lahtonen Dec 16 '18 at 10:31
  • $\begingroup$ I do agree that such questions are common. The way such questions are answered irritates me quite a bit, though. $\endgroup$ – Jyrki Lahtonen Dec 17 '18 at 9:57

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