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Consider these answers (vectors, inequality) on one hand and these (Coupon Collector's problem, angles, arithmetic-geometric series sum, and even alternative CRT approach) on the other.

Why do simple answers gain much more score, while the effort, leading to them, is minimal (like $5-10$ minutes), while full complex answers ($1-2$ hours for each of them except the last) with much effort taken (or when I want to share a specific knowledge or approach), do not receive such positive feedback? It feels much unfair.

In other words, what's going on? Do people just want the math simple (while math is not always this way and sometimes one need to get through to yield a result)? Or am I missing something?
Thanks.

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    $\begingroup$ Keep in mind, voting is not a zero-sum game! If a simple answer gets +10 and a convicted answer gets +5, that’s still +5. And people can vote for multiple answers, even if they choose not to. $\endgroup$
    – gen-ℤ ready to perish
    Commented Jun 9, 2020 at 4:09
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    $\begingroup$ For the same question I prefer a simpler answer compared to an answer based on unnecessarily difficult ideas. Mathematics needs to be made simpler to reach wider audience. A lot of mathematics which is taught in academia is already made unnecessarily difficult. $\endgroup$
    – Paramanand Singh Mod
    Commented Jun 9, 2020 at 12:00
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    $\begingroup$ Not the same people that vote for short answer and longer ones. $\endgroup$
    – user577215664
    Commented Jun 9, 2020 at 15:36
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    $\begingroup$ Writing a short or simple answer can be much harder, and can take longer, than writing a long complicated answer. $\endgroup$
    – MJD
    Commented Jun 10, 2020 at 1:11
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    $\begingroup$ Yes, but also some highly upvoted short answers are rather snarky, and/or meant to impress other knowledgeable users, and not to help the asker, @MJD. $\endgroup$
    – amWhy
    Commented Jun 10, 2020 at 16:20
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    $\begingroup$ +1 to @amWhy for mention of short and impressive answers. Answers should not be for impressing others (well that could be a long long term goal, but not directly) but rather to help askers and to add to the knowledge base of this site. $\endgroup$
    – Paramanand Singh Mod
    Commented Jun 11, 2020 at 13:33
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    $\begingroup$ If a high rep user posts something simple in 5-10 minutes that is one of the things that may trigger a downvote from me. A veteran user should know better and spend that time searching for the duplicate that is highly likely to exist. $\endgroup$
    – Jyrki Lahtonen
    Commented Jun 11, 2020 at 17:53
  • $\begingroup$ Otherwise a simpler answer is better, if one exists (and brings something new to the site). It is unfortunate that so many seek instant gratification. $\endgroup$
    – Jyrki Lahtonen
    Commented Jun 11, 2020 at 17:56
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    $\begingroup$ @JyrkiLahtonen : The search engine here is not simply upto the mark (especially for latex / mathjax stuff). I tend to mark as duplicate mostly those questions which I have answered myself or have added in my favorites/bookmarks. Even then searching in my bookmarks and my answers is a big big pain if I don't remember the exact keyword in the relevant post. Another option is approach0 which does not work on mobile devices. I tried to use it with desktop mode browser setting but it's really not that easy to use. Google is still better. $\endgroup$
    – Paramanand Singh Mod
    Commented Jun 12, 2020 at 3:23
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    $\begingroup$ @ParamanandSingh Even if people only stopped self-plagiarizing here that would be a hige improvement. it may be just me, but I don't understand why anybody would want to view these pages on a mobile. $\endgroup$
    – Jyrki Lahtonen
    Commented Jun 12, 2020 at 3:42
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    $\begingroup$ Proving my point. The asker reposted their question from a year ago with renamed variables. The same user answered it. Copy/pasting the inequality to Approach0 took me three seconds, immediately pointing at three duplicates in AOPS and at this on Math.SE. Neither even tried to search for dupes. This is what pisses me off. $\endgroup$
    – Jyrki Lahtonen
    Commented Jun 12, 2020 at 4:44
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    $\begingroup$ @JyrkiLahtonen: that example was too much. I never expected this kind of thing (asker/answerer pair repeating themselves) although I have myself written almost same or similar answers when I failed in search. I think most of my search limitation which I talk about comes from using the site exclusively on smartphone. $\endgroup$
    – Paramanand Singh Mod
    Commented Jun 12, 2020 at 5:54
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    $\begingroup$ I want to mention that the question I linked to above was closed as a duplicate also by one of the participants. No deletions, though. $\endgroup$
    – Jyrki Lahtonen
    Commented Jun 12, 2020 at 14:22
  • $\begingroup$ @user Hmmm the question is about answers, I didn't consider question simplicity at all. And maybe I want to sum up opinions into one big answer and finally accept it. $\endgroup$
    – Alexey Burdin
    Commented Jun 19, 2020 at 12:00
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    $\begingroup$ Check out this great answer from Did, which is only 1 character long, but has 900 upvotes and 59 downvotes: math.stackexchange.com/a/74383 $\endgroup$
    – Botond
    Commented Jun 21, 2020 at 13:10

11 Answers 11

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One thing to consider is that it is rather reasonable to only vote for answers where one is actually confident that they are correct.

For for more complicated answer the pool of potential voters is thus smaller, and this goes a long way to explain the phenomenon.

The experience you describe is shared by many. Yes, in some sense it is not fair, but it is also hard to avoid, and ultimately the points are not very important. Many a valuable member of the community does not have all that many points.

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    $\begingroup$ This is one of the shortest answers here and got many upvotes (including mine). That kind of dynamics is also seen on main site. $\endgroup$
    – Paramanand Singh Mod
    Commented Jun 11, 2020 at 13:06
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    $\begingroup$ It was also one of the first, or even the first, which is also a frequently relevant factor. $\endgroup$
    – quid Mod
    Commented Jun 11, 2020 at 16:05
  • $\begingroup$ Yes, First answer has some advantage in most cases. $\endgroup$
    – Paramanand Singh Mod
    Commented Jun 11, 2020 at 16:36
  • $\begingroup$ One of my most upvoted answers here is math.stackexchange.com/questions/442472/…, which certainly was not a fast answer ... $\endgroup$
    – kjetil b halvorsen
    Commented Jun 20, 2020 at 5:02
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It's the same reason that detailed essays will never get as many upvotes as cat memes on social media.

On the internet, people consume content primarily in a browsing paradigm. Quick and easy content requires minimal investment from the reader, and is therefore able to capture a wider audience.

This doesn't have to erode the content. Many complex answers would become much simpler with a bit of reorganizing. There is an art to writing with both brevity and precision. You can incorporate this into your own writing by developing a healthy respect for the audience's time and attention.

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    $\begingroup$ But brevity, without quality, is worthless, and some one sentence answers of very low quality get undue upvotes. And just because the internet works that way, doesn't mean it's always a good thing. People don't have to act reflexively; they can reflect, and act more proactively. $\endgroup$
    – amWhy
    Commented Jun 10, 2020 at 14:21
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    $\begingroup$ No link to a cat meme?? I'm sad but upvoted anyway. $\endgroup$
    – hardmath
    Commented Jun 10, 2020 at 15:29
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    $\begingroup$ I sure as heck don't want people voting for the next US president based on a single emotionally-based meme, but rather on concerted efforts to actually read well written essays, follow the news, read the facts, etc. Sometimes there are no shortcuts to the best response. $\endgroup$
    – amWhy
    Commented Jun 10, 2020 at 16:12
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    $\begingroup$ Certainly brevity doesn't imply quality. But I think it's just an artifact of the medium that longer posts get ignored, even if they are of good quality. In the same way, I don't think elections can won on good essays, even if we wish they would be. The well-informed must learn to meme, and meme well, for more casually involved voters to listen. $\endgroup$
    – Alexander Gruber Mod
    Commented Jun 10, 2020 at 18:13
  • $\begingroup$ If you want to discuss this in "whatever quid", I'm game. But you fail to define what you mean when you say to "meme well". So by default, if I present you with an ineffective meme, you will come back with "Oh, they didn't learn how to meme, and meme well"... so you've created a circular argument. But, if you want to discuss this further, I'm always pingable is Whatever quid. But until then, the research in psychology and social psychology + cog sci, wrt the influence from the internet, proves you very wrong: memes induce reflexive, not reflective, actions and beliefs $\endgroup$
    – amWhy
    Commented Jun 10, 2020 at 19:43
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    $\begingroup$ I would say if people learn to write, and learn to write well, then the world would be a better place. $\endgroup$
    – amWhy
    Commented Jun 10, 2020 at 19:46
  • $\begingroup$ US elections getting compared to social media, always a fun read for us Europeans. Seriously, though, why are you bringing politics into this topic? This answer is quite on point IMO. To go through a long/complex answer takes effort and it's not likely I would read it unless I specifically searched for something. Not everything under the heaven is worth my time, no matter its quality. Like US elections - I'd never read an essay on it, but a meme... yes, please. $\endgroup$
    – Ennar
    Commented Jun 22, 2020 at 23:21
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Have you ever had a word limit on an essay? It's not because markers are lazy. It's because brevity focuses the exposition. You may have also noticed short questions are favoured, as long as they're not so short they don't show effort.

Effort is not in general proportional to length; a long first draft often should be shortened in redrafting before it's posted. (This answer was multiple screens at one point.) As Blaise Pascal said, "I would have written a shorter letter, but I did not have the time."

I usually don't leave long answers, as there's a risk of not seeing the forest for the trees, on part of not only the reader but also the writer. Many long answers do get lots of upvotes, but they have to work hard to announce their structure ahead of time. I see proofs as explanations for why something is true; this perspective allows a short answer to help the OP a lot.

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    $\begingroup$ +1 for raising the point about length of an answer. $\endgroup$
    – Paramanand Singh Mod
    Commented Jun 10, 2020 at 6:31
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    $\begingroup$ Sometimes effort is proportional to length. Not always, I grant you, but many times. $\endgroup$
    – amWhy
    Commented Jun 10, 2020 at 16:08
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    $\begingroup$ +1 for the quote of Blaise Pascal. $\endgroup$
    – user577215664
    Commented Jun 13, 2020 at 16:53
  • $\begingroup$ Unfortunately, I have noticed a general trend on MathSE that often, the answers (to MathSE questions, where the OP showed work - reasonably high quality presented questions) are such that the OP will be unsure whether the answer is valid. This same issue presents itself in Math books, where the author island hops from concept to concept, and the reader often has to do a great deal of work to understand why the author is allowed to go from point A to point B. ...see next comment $\endgroup$
    – user2661923
    Commented Mar 28, 2023 at 20:21
  • $\begingroup$ Admittedly, the composition style of a single posting can't please everyone, and experienced Mathematicians will prefer the moderate island hopping. However, the (typically very inexperienced) original poster, will often prefer crystal clear clarity. So, you have the conflict of which target audience to please: the original poster or the typical MathSE reviewer. $\endgroup$
    – user2661923
    Commented Mar 28, 2023 at 20:23
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It’s not always the case. Here is one long, deep answer of mine that got over four times the votes of the next second-most voted, which is short and to the point (and is praised in comments). Here’s a second one, a third one, on integration, one that outvotes the accepted answer.

Granted, these are “old” answers, and looking through my more recent ones, few seem to garner large vote shares quickly, so maybe the demographics and general views have drifted.

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    $\begingroup$ It's not the case, but I can see a pettern. All these answers except the last one have the form 'short answer'+'long rigorous explanation', so maybe it's useful to give a solution outline first. The last one is simply getting the reader involved, even the first theorem is rather simple so one just continue on reading) Thanks for sharing. $\endgroup$
    – Alexey Burdin
    Commented Jun 9, 2020 at 1:48
  • $\begingroup$ Regarding your last sentence about how long ago your examples were written: Perhaps also, back then, answers did not slide down the visible list as quickly as they do these days. $\endgroup$
    – paw88789
    Commented Jun 9, 2020 at 4:17
  • $\begingroup$ +1 but your answer is composed by a short verson and a longer one. So this is another case. I just upvoted it because I really like it. $\endgroup$
    – user577215664
    Commented Jun 9, 2020 at 15:39
  • $\begingroup$ @AlexeyBurdin A pettern is a tavern where one can take their pets, to pet them, while drinking. A pattern, however, is something else entirely. :-) $\endgroup$
    – amWhy
    Commented Jun 10, 2020 at 16:22
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    $\begingroup$ As you can see my English is rough enough to say I'm no native English-speaker (in this life, at least), native English is smooth. But I can understand Russian) Вотъ. Beside that I haven't managed to install any spell-checker yet, that's where the things are $\endgroup$
    – Alexey Burdin
    Commented Jun 10, 2020 at 17:46
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I believe you are simply accusing human nature. It is common for humans to seek out simpler, clearer, more understandable things which minimizes effort. For the most part, this system is very good at getting rid of unnecessary work, but it will have flaws like everything does. I'm sorry this upsets you; I hope you find some acceptance in it sometime.

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  • $\begingroup$ I can see how that could be a factor suggesting that questions where finding answers is easy get more answers (or get answers sooner) than do questions where answering them is harder. But I don't see how it has anything to do with how come, if a question has a short answer and a long one, the short one tends to get more upvotes. $\endgroup$
    – Rosie F
    Commented Jun 14, 2020 at 7:37
  • $\begingroup$ @Rosie F Perhaps the shorter answer was clearer and more helpful to the person asking the question. In other words, less convoluted than the long answer. $\endgroup$
    – Tauist
    Commented Jun 14, 2020 at 7:40
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Some of the short answers read as very "smart"; although usually, whether they are really so is arguable, people seem to like "smart" answers. See some extreme examples like this and this.

Why do simple answers gain much more score, while the effort, leading to them, is minimal...

If you find it "unfair", think about it in this way: writing down quickly a very short answer seems effortless; being able to do so may require lots of efforts behind the scene. Moreover, length is not in general equivalent to quality. Some questions can really be answered in one word that is comprehensible.

In general, length is not equivalent to quality.

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    $\begingroup$ And yes, that's why I didn't mention this answer in the list of short ones as it requires training (like to prove why identity in a group is unique or that a inverse is unique or that right inverse equals left one and bunch of similar excercises) and thinking (the first idea was considering $S=T^{-1}ST$ but it's not given that $T$ has inverse), but became quite short) -- as it's not this case. $\endgroup$
    – Alexey Burdin
    Commented Jun 9, 2020 at 18:31
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    $\begingroup$ +1 for the last link. $\endgroup$
    – hardmath
    Commented Jun 10, 2020 at 12:44
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    $\begingroup$ But most short answers are fairly effortless; there are occasions where brevity and being "spot on" merge. But this is generally not the rule on this site. $\endgroup$
    – amWhy
    Commented Jun 10, 2020 at 16:10
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    $\begingroup$ @amWhy: I doubt that. Do you have any data? $\endgroup$
    – user9464
    Commented Jun 10, 2020 at 16:11
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    $\begingroup$ Yes, I could show you many examples from two of the most highly upvoted answerers on math.se, who get votes due to their rep and academic stature/positions, but regularly answer their questions in one or two sentences, which rarely answer the questions they propose to answer. Other factors besides quality of post, are implicated in many such upvotes. I really love a brief answer, when it is possible; such answers are precious; but not all quality answers to questions can be brief. That's all I'm saying. $\endgroup$
    – amWhy
    Commented Jun 10, 2020 at 16:17
  • $\begingroup$ I see your point in a way. Unfortunately it seems to me that more often a quick answer is an indication that the question was so easy that the answerer wasn't taxed at all, and the effort behind the scene amounted to turning a crank twice. $\endgroup$
    – Jyrki Lahtonen
    Commented Jul 9, 2020 at 8:33
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Time intervals between question and answer:

(Note that in the case of the CRT question, no answer got more than 1 upvote, and one answer got none.)

More data is/are needed (and should be easy to collect), but I suspect that the culprit is our old friend The Fastest Gun in the West.

At the very least, time is a confounding factor, which needs to be allowed for before one can conclude anything about simplicity versus complexity.

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  • $\begingroup$ browser: firefox, alt hovering text on gray "2 days ago" near the user icon of question/answer. html reads like this: <span title="2020-06-11 12:45:19Z" class="relativetime">12 mins ago</span> $\endgroup$
    – Alexey Burdin
    Commented Jun 11, 2020 at 12:58
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    $\begingroup$ This fastest gun problem is real on math.se. For questions that are really interesting (to me) I read all answers and often get some beautiful gems buried down with just few upvotes. Sad but I can contribute only one vote. +1 $\endgroup$
    – Paramanand Singh Mod
    Commented Jun 12, 2020 at 18:30
  • $\begingroup$ As I think I mostly answer questions that have been around for hours or days (with or without answers), I may possibly be The Slowest Gun in the West! $\endgroup$
    – Calum Gilhooley
    Commented Jun 12, 2020 at 18:39
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I think it has to do with "Occam's razor". Basically it says that people prefer simple hypothesis (answers in this case) rather than complex and slightly better hypothesis.

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    $\begingroup$ Occam's Razor says that Nature prefers simple hypotheses. But Nature doesn't have an account on math.stackexchange. $\endgroup$
    – Gerry Myerson
    Commented Jun 13, 2020 at 7:55
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    $\begingroup$ I wasn't aware of rephrasing of Occam's razor principle "the simplest solution is most likely the right one", then I did continue reading wiki, jumped to ad hoc hypothesis, then to dark energy, expansion of the universe, ... and ended up on Krylov-Bogolyubov theorem. Thank you so much for this wonderful wiki journey. @sudddddd $\endgroup$
    – Alexey Burdin
    Commented Jun 16, 2020 at 17:19
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  • Its easier and faster to create a short answer. Maybe the effort is less but not always (e.g. thinking of a clever trick vs blind application of laplace transform tables). Its always easier to type. Such answers will appear more often and be seen more often, and be able to be voted on more often, and usually before the long answer appears.

  • Voting may seem quite fine grained but each person only gets to vote each answer once. Maybe I like the high level approach but I really like the long answer with dirty details, what am I to do?

  • when you ask "Do people just want the math simple", the answer is actually yes, as simple as possible. When its not possible you can only get long answers which can get a lot of votes, e.g. some hard contour integrals. If you want to post a long answer that covers a general case when a simpler answer would answer the question as stated, please do, but you need to understand that you may be doing it for a smaller audience (maybe even an audience of size 1, yourself, who can't vote for your answer).

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Because for me it makes it easier to find whether I am looking at the right question, which sometimes is not as the title suggests.

As a user, when I look at an answer, I skim over all available answers to see, if there's anything I haven't tried which is easier in case of simple structured answers and decide if I need to look somewhere else.

And as a contributor, I suggest to structure the answer as simple and on point in the first part, extended with the details for those who wants to explore more. If your answer is correct and helpful, it will get the upvotes anyway.

Structure your answers can be:

Simple Answer with Illustration if needed

Detailed Explanation for more curious ones

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In principle, upvotes denote a useful answer.

A useful answer is one which is to the point and avoids spreading irrelevant details.

Double bonus if the answer is elegant, i.e. simpler than other relevant answers.

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