up vote 8 down vote favorite

When I posted different answers to a question, some people seemed to frown upon it.

Is G/pG is a p-group?

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I don't think there's anything wrong with posting as separate answers, if the strategies taken in the different answers are "sufficiently different". Unfortunately, "sufficiently different" is somewhat subjective... – J. M. Nov 8 '12 at 6:56
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@J.M. I think the three answers to the linked question are very different in the strategies. – Makoto Kato Nov 8 '12 at 7:29
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@MakotoKato : hence J.M. wrote 'Unfortunately, "sufficiently different" is somewhat subjective.' The people who voted/commented may disagree with you. – Willie Wong♦ Nov 8 '12 at 8:50
@WillieWong In that case, what's wrong with posting several answers which are not sufficiently different? – Makoto Kato Nov 8 '12 at 8:54
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Like you were already informed: this is looked upon as "reputation farming", a way to game the system. Some people see it as the same as trying to get paid twice for doing the work once. Seriously though: the users already quite clearly explained their reasons to you in the comments. You seem to be just unwilling to listen and appear to be just shopping for second opinions... – Willie Wong♦ Nov 8 '12 at 9:02
@WillieWong Please define reputation farming and explain why it's wrong. – Makoto Kato Nov 8 '12 at 9:20
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@Makoto: I quote: "Some people see it as the same as trying to get paid twice for doing the work once." Or, as Cameron Blue described for you: "Trying to get more reputation by posting several answers [to the same question]." I am starting to get the feeling of déjà vu about the shape this conversation is taking on. – Willie Wong♦ Nov 8 '12 at 10:58
@WillieWong I don't see why it's trying to get paid twice for doing the work once. They are essentially different answers. – Makoto Kato Nov 8 '12 at 11:18
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@Makoto: I refer you to my earlier comment. I'll excuse myself from this conversation now unless you ask a question whose answer I haven't already provided. – Willie Wong♦ Nov 8 '12 at 11:21
@WillieWong Let me ask the same question I asked robjohn. What about posting an answer to a question which someone else already answered? There is nothing wrong with doing so, as long as they are sufficiently different? – Makoto Kato Nov 8 '12 at 11:24
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What exactly are "independent answers"? – Michael Greinecker♦ Nov 8 '12 at 13:59
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I think I've posted more than one answer to the same question a few times. No one's complained to me about it. – Michael Hardy Nov 14 '12 at 0:50
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My experience has been the same as @MichaelHardy's. I wonder if part of the difference is that fewer people trust Makoto Kato's good faith. – MJD Nov 14 '12 at 3:41
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@MJD Are you implying that there is a good reason for people not to trust my good faith? – Makoto Kato Nov 14 '12 at 16:34
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@MakotoKato I am only implying that fewer people trust your good faith. Surely you were already aware of this. – MJD Nov 14 '12 at 17:30
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6 Answers

up vote 13 down vote

When answers legitimately take different approaches, separate answers are usually better since they each come with different direct links and comments sections.

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up vote 13 down vote

One reason for preferring a single answer is given when you try to add another answer, which suggests refining and improving an existing answer.

The answers you gave are not especially distinct from one another. By combining them into a single answer, the relationships between them can be seen implicitly through juxtaposition -- or even better, it could be explained explicitly. The combined answer could easily be much more illuminating than three individual answers.

I imagine that the answers aren't especially distinct aggravated the negative reaction to multi-answering.

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"The answers you gave are not especially distinct from one another." (1) is based on the fundametal theorem of finitely generated abelian groups. (2) is based on the theory of vector spaces over a finite field. (3) is based on the Cauchy's theorem. This proof also can be applied to a non-abelian finite group all of whose elements have a prime power orders. How come those are not especially distinct from one another? – Makoto Kato Nov 10 '12 at 6:49
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At the highest level, the theory of vector spaces over $\mathbb{F}_p$ is identical with the theory of abelian groups with exponent $p$. --- In the situation of the post, the structure theorem for f.g. Abelian groups is the same thing as the theorem that finite-dimensional vector spaces have a basis. --- In fact, you could swap the first sentences of (1) and (2) and still have answers at the same level of rigor as the originals. --- Answers (1) and (3) are both just "every element has order $p$". They only look different because of the (unnecessary) argument surrounding them. – Hurkyl Nov 10 '12 at 11:31
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The fundamental theorem of finitely generated abelian groups has nothing to do with the theory of vector spaces over a finite prime field. (1) is based on the former and (2) is based on the latter. – Makoto Kato Nov 10 '12 at 19:24
up vote 12 down vote

Doctor, it hurts when I do this

You're getting some push-back for something you're doing on the site. The feedback from other members prompted you to ask this question, but even prior to that the software itself gave you a bit of resistance when you went to add that second (and third) answer:

Are you sure you want to add another answer?

You could use the edit link to refine and improve your existing answer, instead.

Of course, it is allowed - there are times when it's very useful - but they're not common; generally, you do want to just edit your existing answer.

If you want feedback on your actions, explain their purpose

Let's ignore the abstract question here. As robjohn and Bill have pointed out in their answers, there are occasions when multiple answers are useful, and (many more) occasions where you really just want one answer. But that's not what you asked. You linked to your multiple answers, and a cursory examination makes one thing blatantly obvious:

You aren't making any effort to explain why one answer might be preferable to another.

There are often multiple ways to solve a problem. One of the big advantages of the Stack Exchange system is that, when posted as separate answers, the most generally useful solution can be ranked higher by those reading than the rest. However, this falls apart when there is effectively no difference, or when the difference is subtle. So... Which is it? You must've had a reason for bothering to write multiple responses - yet you didn't bother to include that reasoning in the answers themselves. It's almost as though you expect others to do this for you...

Asking - and answering - in good faith

Indeed, this meta question suffers from the same problem. Right before asking it, you posted this comment below one of your answers, in response to specific criticism of your answering strategy:

@CameronBuie Maybe someone would down vote for a false proof. This is only an example. There are other confusing factors. As for your last comment, I didn't get any reps. Anyway, what's wrong with separate answers? – Makoto Kato

Uh, yeah, maybe that would happen. Is that what you hoped would happen? Being unsure of one or more of your proofs, you posted them separately so as to elicit specific critiques of each? Then why not say that? And when raising the discussion of a specific scenario here, one already under discussion elsewhere, why not summarize your already-stated rationale for doing what you're doing, rather than leaving folks to debate the general case? There's a time and a place for everything - but what you're really concerned with here is, was this the right time and place for multiple answers?

Frankly, I think you would garner a lot more sympathy - or at least understanding - if you were a bit more transparent as to your intent when you engage in activities that are uncommon on this site. Don't assume that others will assume good intentions on your part, and you may find they're a bit more likely to do just that in the future.

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"You aren't making any effort to explain why one answer might be preferable to another." Because that's irrelevant to the title question. As the title shows, I took it for granted that the three answers are essentially different. I also took it for granted that showing different approaches to a problem is a pedagogically good thing. – Makoto Kato Nov 10 '12 at 21:37
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If you were also the one voting on them and questioning their separation, then your assumptions would suffice. However, not everyone shares those assumptions. When you encounter clear evidence that this is the case, it becomes necessary to mention them explicitly. – Shog9♦ Nov 10 '12 at 21:40
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@Makoto: To reiterate what has been told here, and countless times before, you cannot expect to be using the site in your own way without upsetting people. The fact that people tell you that something is not usually done means that you should probably justify it, at least at first. Furthermore, it is sometimes good to try and understand the other side and not just claim that this is just their opinion and you can do whatever you want. The main thing about a community is that it is based on several people, and note the similarity between "community" and "communication". – Asaf Karagila Nov 10 '12 at 22:57
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@Asaf I agree that it would be helpful to give some hint as to the motivation for separating the answers. But I don't think it should be required. I have posted multiple answers occasionally as have many other users, and not always with such motivation (often it is "clear"). But I don't recall any of those answers being criticized like MK's. Nor do I recall even a single instance where those multiple answers raised any doubts in my mind that they were posted to farm rep. That's not to say that might never occur. Rather, I think we need to judge such matters on a case-by-case basis. – Gone Nov 11 '12 at 0:02
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Huh, this is actually a very level-headed answer. Why the downvotes? – J. M. Nov 11 '12 at 1:07
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If you read the answers, it's clear that they are based on different ideas. I don't think it's necessary to say so. – Makoto Kato Nov 11 '12 at 1:15
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Way I see it, here's what Makoto seems to have trouble comprehending: if he wants to use the site in his own peculiar way, he ought to not be surprised that other users are reacting in their own peculiar ways to whatever he's producing... – J. M. Nov 11 '12 at 9:57
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@Bill, oh I certainly have posted multiple answers in some questions myself, so no need to throw that particular rock at me. What I'm saying is, it would seem that the answers being "sufficiently different" was not sufficiently justified from the viewpoint of whoever voted his answers. So, he shouldn't be so surprised. I mean, people actually had the courtesy to explain why they did what they did with respect to votes; that maybe is something to be stunned about. – J. M. Nov 11 '12 at 10:48
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@Bill: regardless of how other instances have been received, it's indisputable that this case produced an unacceptable amount of confusion - both on the part of the asker, and the other readers. No matter how acceptable a technique might be in theory, when it doesn't work in practice it's time to revisit your assumptions. – Shog9♦ Nov 11 '12 at 19:10
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@Shog9 That's only because of the OP's recent history. Had it been any other author, probably we would not be having this meta discussion - just like we did not in the past. – Gone Nov 11 '12 at 21:38
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@Bill: There's a big qualitative difference between lots of users each engaging in a little edgy behavior and a single poster engaging in a lot of edgy behavior. – Hurkyl Nov 11 '12 at 22:14
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@Makoto: You were told many times before that your actions have cost your reputation (not the one in points, but rather the one you cannot quantify) as a member of this community. You cannot possibly be surprised that people still tend to be slightly more rigid with you than they would be with others. You have to work very hard to repair that broken reputation of yours, and by arguing with people constantly you're not helping yourself. – Asaf Karagila Nov 12 '12 at 21:16
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@Makoto: The first thing you did after joining this site was to use it wrong. The next thing was to insist that you are using it right. Only after so many people gave up on trying you agreed to some mitigating solution, but you still insisted on doing things your way. Now say I come to visit your house, and I walk in with boots full of mud. I mess up your entire flat and leave muddy prints all over the sofa. You may be angry and I will insist this is just your opinion that I shouldn't do that. But will you invite me again? Especially if I won't apologize and promise to behave? I doubt that. – Asaf Karagila Nov 12 '12 at 21:27
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@Makato: on the question with Mariano's answers you linked to? No close votes, and all the comments are visible. On the question you answered, and linked to here? Yes, there was a lot of confusion, which calmed down after you explained yourself. Which is my point: when you encounter confusion, explain what you're doing - so many problems can be solved with just a bit of effort put into communication! – Shog9♦ Nov 12 '12 at 21:37
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@Makoto: Be careful about treating all negative feedback as evidence of some sort of witch-hunt though; I hardly think everyone involved here sits around waiting for you to do something so they can pounce on you. Yeah, there are probably folks who take an unnecessarily dim view of your efforts, but there are just as surely folks who simply care about the site and its community and wish to see problems resolved. – Shog9♦ Nov 12 '12 at 22:45
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up vote 7 down vote

Usual cases

There is nothing wrong with giving multiple answers, as long as they are sufficiently different. However, it is customary to give them all in the same post, headed by a bold title and separated by a line ***.

Exceptional cases

If one of the answers is very long, it might be necessary to make an additional post, but that is a very exceptional case.

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What about posting an answer to a question which someone else already answered? There is nothing wrong with doing so, as long as they are sufficiently different? – Makoto Kato Nov 8 '12 at 9:40
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Absolutely not. As long as they don't duplicate each other; the more, the merrier! – robjohn♦ Nov 8 '12 at 13:32
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I prefer separate answers in separate posts. – Graphth Nov 8 '12 at 17:18
@robjohn Even if he is reputation farming? – Makoto Kato Nov 9 '12 at 2:05
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@MakotoKato: I would not call a good answer for a question, whether or not someone else has already answered, reputation farming. – robjohn♦ Nov 9 '12 at 2:26
@robjohn Please explain why you demand sufficient differences in multiple answers by a user while you don't care about it with an answer to a question which someone already answered. – Makoto Kato Nov 9 '12 at 3:06
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@MakotoKato: Not all social behavior can be quantified into a well-defined list of laws. In fact, most of it can't. Human beings are just this sort of wonderful creature that develop a big brain exactly for this purpose: to understand what is the community norm without having a flowchart which defines completely everything. Your incessant requests for "definitions" are almost always impossible to counter without shrugging and giving up (as many people do, if you look at the comment histories of your various threads). – Asaf Karagila Nov 9 '12 at 7:59
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@MakotoKato: I thought it had already been decided that the answers considered, whether from a single or multiple users, were "sufficiently different". – robjohn♦ Nov 9 '12 at 12:04
@robjohn I think I misunderstood you. I'd like to withdraw my last comment. I'm sorry about that. – Makoto Kato Nov 10 '12 at 10:06
Could you give us some supporting evidences of your claim that it is customary to give them all in the same post? – Makoto Kato Nov 11 '12 at 21:15
@MakotoKato: I would have to spend more than I have right now to find more, but here is one – robjohn♦ Nov 12 '12 at 1:38
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@MakotoKato: I would consider the approach of those answers suffuciently different. Algebra, algebraic geometry, and two geometry (the two geometry might be a bit close, both using localization properties of invertible affine maps). In any case, I don't get the impression that Mariano was reputation farming. – robjohn♦ Nov 12 '12 at 20:31
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@Makoto: Are you capable of seeing the difference between three long answers and three two lines answers? (Hint: it's the length of the answers) – Asaf Karagila Nov 12 '12 at 23:04
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@MakotoKato: I would say that it is a combination of size and uniqueness, and it is hard to put a quantitative cutoff on things like uniqueness. – robjohn♦ Nov 13 '12 at 18:24
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Since I did not vote on your answers, that would be off topic here. – robjohn♦ Nov 14 '12 at 16:49
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up vote 6 down vote

There are various honorable reasons that one may have for posting more than one answer to a question. For example, often I am interested in judging how well-known various approaches are, so that I can use that feedback to revise my teaching methodology. This is more difficult to do if one places multiple answers in one post since then it is not clear which particular answer the votes and comments target (which, by the way, is a huge problem with votes on multiple-answers on meta).

For a concrete example, I explicitly chose not to place the well-known degree-based approach into my answer on why polynomial rings are not fields, because I sought to determine what sort of response the given universal approach would receive. The surprisingly large number of votes it received (along with the tone of the comments) helped provide further evidence to confirm my suspicion that many algebra textbooks do not effectively teach such universal ideas.

It is important to keep in mind that - in this way - the site provides useful feedback to teachers. Having sharp modular boundaries between logically independent answers serves to optimize the value of such feedback. This allows teachers to learn as well as teach, which provides much further motivation for teachers to participate. And, of course, the more teachers we have participating, the more the site will prosper.

Another reason for posting multiple answers is to draw modular boundaries between knowledge levels. Sometimes I post answers that include both elementary and advanced perspectives on topics. These combined posts often receive fewer votes than if I separate the answer into an elementary post and an advanced post. Probably this is because the advanced parts scare away those with no knowledge of the advanced topics, so they stop reading - mistakenly believing that the entire post is too advanced.

Similarly, students may have honorable reasons for posting multiple answers in separate posts. For example, a student with two answers may be confident of the first, but may have doubts about the second answer. Thus it makes sense to post the second answer separately, so that feedback on it can be appropriately isolated. Otherwise, if both answers were combined into one post and the second answer had problems, then the combined answer might receive a mix of upvotes and downvotes, which might relay false impressions about the first answer, e.g. misleading readers into thinking that the first answer also has problems. Further, the first answer might not get elevated to the proper level of exposure, possibly leaving an inferior answer to be the highest-voted.

Generally, readers may desire to upvote some answers and downvote others, which is not possible if they are all combined into one answer.

Finally, one tangential point is worth emphasis. Before one leaps towards accusations such as "reputation farming" etc, it is important to keep in mind that not everyone pays attention to reputation, so it may not even occur to some folks that posting multiple answers might be viewed that way. Indeed, some of us are here simply to share our knowledge of mathematics, and have been doing so for years in other forums (e.g. usenet newsgroups) where reputation plays no role. Please try to keep in mind the diversity of our community before jumping to possibly unfounded conclusions about such matters.

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There are also some people who do not care about money. Should we allow people who don't care about money to get free money as long as they need? No. It is true that some users don't care about reputation, but others can. I would hate to think that we should give a precedent case of posting multiple answers just because someone doesn't care about reputation (or so they say). I do agree that there are reasons for posting several answers, though. I haven't looked at the specified question, so I cannot tell about this one, though. – Asaf Karagila Nov 8 '12 at 16:51
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That analogy is not appropriate. Multiple independent answers don't get free upvotes. Each answer still has to earn its own upvotes (or downvotes). The point of my tangential remark is to encourage others to show some empathy when attempting to understand the motivations of others. Some of our users are not motivated at all by the rep game, and it is essential to keep that in mind when evaluating such matters. – Gone Nov 8 '12 at 17:09
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@AsafKaragila Then don't upvote it. – Graphth Nov 8 '12 at 17:33
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@AsafKaragila I don't really understand the relevance of yours. Bill is saying there are reasons to do separate answers. You reply and say we shouldn't believe any one who says they are not in it for reputation. If people who don't care about money do work to deserve the money, then who cares if they get it? They did the work to deserve it. Why are we so concerned with people getting reputation? It's not like any one is gaming the system and ending up as one of the top users on here because of it. They may game the system and end up with an extra hundred reputation per month. – Graphth Nov 8 '12 at 17:42
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@Asaf You wrote: "Reputation is a driving force, regardless what anyone says..." That may be true for you, but you cannot speak for others. Some of our most prolific contributors participated in sci.math for years/decades without any rep motivation whatsoever (there is no rep capability in usenet newgroups). I suspect that, like I, most of those folks are little-motivated by rep. Instead, they are surely primarily motivated by teaching. – Gone Nov 8 '12 at 17:54
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@Bill: Sheesh, you are such a condescending person. It is impossible to speak with you without getting angry. It is a tangential point, but I feel that you are impossible to reason, discuss or argue with. You have set your mind and nothing can change your opinion. I feel ashamed to have a person like you to hold any power within this site. I am not going to reply to your comments again here, or elsewhere. – Asaf Karagila Nov 8 '12 at 17:57
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@AsafKaragila I'd rather have two sufficiently different answers neatly organized as two separate posts. That's more important to me than worrying about whether or not someone is gaming the system. So, if it's borderline, I'd rather someone neatly organize things than worry about whether or not some users are going to accuse them of rep farming. That is, a user shouldn't have to think "Hmm, are people going to think I'm gaming the system if I do this" if they honestly aren't. And, other users should give the benefit of the doubt so that honest people don't worry about this. – Graphth Nov 8 '12 at 18:05
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@Bill: I could just as easily say that a lot of tension would vanish if people stopped countering valid issues with platitudes. Problematic behavior done with good intentions is still problematic behavior. If you really want to give benefit of doubt, then assume Asaf's intent is to actually worry about problems rather than to be misanthropic or whatever else you are assuming, and react accordingly. – Hurkyl Nov 8 '12 at 23:31
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@Bill: Non-problematic behavior is non-problematic. I agree that there are differences in opinion. The part I find insulting is the implication that we shouldn't even contemplate whether behavior is problematic, because some people behave that way with good intentions. Empathy for people who engage in (possibly) problematic behavior is fine -- but don't let that cloud your judgment of the behavior. Similarly, you should have empathy for people who are actually out there trying to judge things fairly; your tangential remark is rather patronizing, and it suggests the aforementioned insult. – Hurkyl Nov 9 '12 at 9:30
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@Bill: And I'm concerned about alienating users who would speak out with honorable intentions about perceived problems. Just as you (rightly) point out that such people can cause harm if they act carelessly, I assert that you are causing harm by being similarly careless (if I give you the benefit of the doubt, anyways). While these implications may not have been in your intent, they are present in your words, and it is your words that are the content of your answer.... – Hurkyl Nov 10 '12 at 0:01
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.... Additionally, special care is needed for such comments, because of how commonly they are used to bully those who would offer objections or criticism. A lot of ill feelings arise when people are led to believe their opinions and arguments are being drowned out -- or even vilified -- by gratuitous warm and fuzzy sentiments. – Hurkyl Nov 10 '12 at 0:10
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@BillDubuque Your internet experience doesn't seem to translate to the ability to state your opinion in a way that does not offend or alienate others. The problem is exacerbated by you having a history of actually insulting other users outright. – Michael Greinecker♦ Nov 11 '12 at 9:29
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@Bill There is no insult among you comments here, but very bad wording. "Apparently, That may be true for you, but you cannot speak for others." begs to be read as Asaf being a rep-w&/%e. The remark "I suspect that, like I, most of those folks are little-motivated by rep. Instead, they are surely primarily motivated by teaching." can allude to Asaf not caring about teaching. Of course, one does not have to interpret things this way, but internet experience should teach you how to phrase things better. – Michael Greinecker♦ Nov 11 '12 at 9:53
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@Makoto: If your answers are "pedagogical" why are there no explanations? Why are the answers concise and lack actual explanations? If the answers are for future readers (including the future OP) how would voting help you establish any reasonable input over which approach is preferable? – Asaf Karagila Nov 11 '12 at 22:15
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@Makoto: Your comment is off topic. This meta topic isn't about whether people should provide different approaches to a problem. This meta topic is about if and when a person providing different approaches should put them in a single answer. – Hurkyl Nov 11 '12 at 22:17
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up vote 2 down vote

One reason we sometimes see multiple answers to the same question is some doubt as to the mathematical knowledge or experience of the person who has asked the question.

In such cases I think it is of general benefit to the person who has asked the question - and to future explorers of the site - to have the links between levels indicated.

My oldest daughter (aged 15) said to me yesterday - when I ask you about homework you often go off onto things I haven't learnt yet, and which I don't quite understand - but then when my teacher deals with them in class, I do get them, and my classmates don't. She was pondering why that was, and I was thinking - it's how I learned mathematics - from my dad.

This is a great site for sensing the direction of travel and the challenges ahead.

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That is one of the reasons that I mentioned in the fifth paragraph of my answer. I wholeheartedly agree about links. I've probably posted almost as many links as answers (a couple thousand), since I believe that showing the diverse and beautiful interconnections in the mathematical web is one of the great pedagogical values that this site has to offer vs. other learning resources (e.g. paper textbooks, which are limited by linear organization). – Gone Nov 11 '12 at 22:40

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