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I was going through the 'frequent' section in "All Questions" on MSE, and I was surprised that some questions like [How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$? ] has around $300$ upvotes and $200$ favourites.
It makes sense to favourite a question as there were many good answers on that question and they may want to revisit a famous question, but why did people "upvote" that question? There wasn't even any specific research done for that question too.

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    $\begingroup$ The post has 68,000 views; fewer than 0.44% of readers have upvoted it. It's about the hundreds or thousands of early calculus students that see this addressing their question, not about whether the question is high-quality. $\endgroup$ – user296602 Sep 18 '17 at 21:10
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    $\begingroup$ But views are also considered from users not signed in, isn't it? Anyway, I guess your logic makes sense $\endgroup$ – john doe Sep 18 '17 at 21:15
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    $\begingroup$ If you haven't noticed before, it seems you are now encountered the fact that highly positive vote scores for questions (and for answers) do not necessarily correlate to the quality of question (answer), it's difficulty, nor even to the effort put in by the asker (answerer). In some ways, people some people use upvotes as "like" votes: and it is typical to find that lots of answerers answering a question each tend to upvote the question they're answering, and when lots of answers exist, and then, where there are quickly escalating upvotes, they breed more upvotes: a "me too" effect. $\endgroup$ – amWhy Sep 18 '17 at 21:15
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    $\begingroup$ My two most highly upvoted answers (to two very highly upvoted questions) do not reflect my best work. One emerged out of a sincere reflection of a "real-life" relation with certain properties (hmm... sleeping with (innocently)), and a simultaneous realization that my "hit" could also be read in a different, less innocent way, too. The second was an arithmetic question. I would not point any one to those questions or answers as exemplars of great thoughtful questions, or great illuminating answers. $\endgroup$ – amWhy Sep 18 '17 at 21:21
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    $\begingroup$ Once the number of answers increase to 5, 6, or more, then votes for onlookers become a "comparison game." One person may think "these two answers a way better (or matching how I would have answered) than the others" and then upvote the two "way better" answers. And another onlooker may review the answers 30 seconds after the first, and think, "Hmm, why do these two answers have more upvotes, when I think that at least three others are better!" And then proceed to upvote the three they thought had been overlooked. And on, and on... $\endgroup$ – amWhy Sep 18 '17 at 21:32
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    $\begingroup$ And I think this can occur in the opposite direction too, in terms of downvoting questions: virtually identical questions posted a month apart, or at different times of the day, can be received in radically different ways: one may not get any up nor downvote, or maybe even an upvote, while the other may receive a score of -8. I think in both cases, high upvoting, high downvoting, it helps that, while some of the counts may be a valid reflection of quality, some may be rather arbitrary. $\endgroup$ – amWhy Sep 18 '17 at 21:36
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    $\begingroup$ Oops, sorry all, perhaps I should have just written an answer! $\endgroup$ – amWhy Sep 18 '17 at 21:47
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    $\begingroup$ @amWhy Clearly, you understand this phenomenon, so why do you criticize when it happens on another site? $\endgroup$ – Mark McClure Sep 18 '17 at 23:39
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    $\begingroup$ Dear @MarkMcClure : it seems the subject matter of the two posts (banal content vs 'easy' content) is not as similar as your comment suggests. I don't really understand how your comment contributes the the discussion at hand, either. Perhaps you could consider removing it. Regards $\endgroup$ – rschwieb Sep 19 '17 at 2:31
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    $\begingroup$ I don't like the fact that this answer of mine is my second most voted answer and made me earn my first golden badge (the populist badge), but I guess it's, at least in part, because it is easy to understand. $\endgroup$ – José Carlos Santos Sep 19 '17 at 9:11
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    $\begingroup$ @MarkMcClure I think the comparison falls rather flat for the reason I mentioned, but you're free to stand by it. Regards. $\endgroup$ – rschwieb Sep 19 '17 at 9:20
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    $\begingroup$ Since nobody's brought it up yet: look up the bikeshed problem. $\endgroup$ – J. M. isn't a mathematician Sep 19 '17 at 14:38
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    $\begingroup$ The most important con that I see with this type of questions is that they attract wrong (and even utterly wrong) answers. For example, in the question you linked there are at least like 5 wrong answers. $\endgroup$ – Xam Sep 23 '17 at 4:27
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    $\begingroup$ I'm surprised no one has mentioned question age, or maybe I missed it. The example linked to in the question is almost six years old. It's unlikely that question received that many upvotes in a short time and then had no activity afterwards. Proving that limit is not easy for the typical Calc 1 student, and I bet a good portion of the upvotes that question received is from Calc 1 students coming across it over the years. I noticed a lot of these easy/basic/introductory-type questions with the high upvotes are from 2011 give or take a year. $\endgroup$ – user307169 Sep 23 '17 at 15:47
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    $\begingroup$ On a slightly different tack - while the body of the question thankfully goes a different direction, it's very easy to conflate 'easy' with 'bad'. An easy question is by no means innately a bad one, and a difficult question is not innately interesting; they're two distinct axes, mostly orthogonal to each other. $\endgroup$ – Steven Stadnicki Sep 25 '17 at 16:46
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Voting on questions frequently has little to do with the amount of research that the asker has put into it, or the objective quality of the question. Questions that are easier to understand for a broad audience get more votes than technically difficult questions. Questions that address popular issues (e.g. geometric series, basic limits or identities, and so on) tend to get very many views, which translates into these incredibly high vote counts. For comparison, this question addresses a common issue on the internet that is very easy to understand; barely 1% of readers expressed an opinion on the post via voting, yet this translates into almost 600 upvotes. There's also a tendency to pile on, especially when questions make it to the hot network list; people think "huh, that's neat" and upvote without paying much attention to more local site culture.

The same issues apply to answers. The third highest voted answer on the site is a single character. Here is another answer that is not at all technical, but is easily understood by a broad audience, and happens to be attached to a question with 457,000 views.

So in short, the easiest way to get a ridiculous number of upvotes is just to be seen by tens of thousands of people, and hope that half a percent of them make their opinion known. The 1% rule is very relevant here.


*Note for all of these; I'm not singling out these questions or answers because I have any issue with them per se, but only because they seem to support my claims.

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    $\begingroup$ dat single character answer tho! $\endgroup$ – john doe Sep 18 '17 at 21:57
  • $\begingroup$ Another massively upvoted question from primary school -level mathematics also exists (because it was spread over the internet (or over SE) and which was understandable to most): math.stackexchange.com/questions/379927/… $\endgroup$ – amWhy Sep 18 '17 at 22:02
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    $\begingroup$ @amWhy That one is particularly interesting because there are also a lot of adults who don't think about the fencepost problem until they're directly faced with it when coding something. $\endgroup$ – user296602 Sep 18 '17 at 22:03
  • $\begingroup$ One aspect that I think is very appropriate in mega upvoted questions with megaples of answerers who answer, and extremely wide exposure (as a Hot Network Question, etc) is making such posts "community wiki", as was done in one of the questions linked in the answer: math.stackexchange.com/questions/733754/…. I think such posts should remain, as historical, but at some point, may be most appropriately changed to community wiki. $\endgroup$ – amWhy Sep 18 '17 at 22:14
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    $\begingroup$ Simple souls equate the very low number of characters in an answer with a low amount of thought put into it. In case of the W answer, I already explained somewhere that the identification does not hold. At first the explanation was even in the first comment to the answer but an unfortunate deletion of the whole comment thread by a mod made it disappear. Anyway, let me suggest to reconsider the meaning of the case. $\endgroup$ – Did Sep 19 '17 at 6:04
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    $\begingroup$ @Did Honestly that $W$ is a really bad answer. It is so hard to understand what you mean by that $W$. I don't understand why you will write such a vague answer considering your reputation and the fact that you are one of the first users to critise people like Dr. Sonnhard for writing vague answers. Please consider editing that answer. $\endgroup$ – A---B Sep 19 '17 at 19:35
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    $\begingroup$ @A---B You must be kidding. $\endgroup$ – Did Sep 19 '17 at 19:41
  • $\begingroup$ The post I linked to above (second comment below user296602's answer), to be fair, also includes an uploaded worksheet, in which the asker answered the question correctly, but it was marked wrong by the asker's teacher! (The teacher needed a lesson from the student in that case!) To me it represents that votes aren't necessarily about an objective question and its answers, but rather, that linked post gave users (on this site and beyond) a chance to revel in the mistake by a teacher. $\endgroup$ – amWhy Sep 20 '17 at 18:29
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    $\begingroup$ Similarly, humor, or a particular way of phrasing an answer that draws folks in, challenges many (who might at first be puzzled or confused by the answer at first), until they get the Aha! moment, after which they upvote the answer. It seems A---B may have stopped short of ever reaching Aha! in @Did's answer, e.g. That's to bad, because the one letter answer, W, explains/reveals what might take most an entire page to explain. And, pedagogically, it is awesome, because it requires the asker, and anyone reading the answer, to think a wee bit! OMG! $\endgroup$ – amWhy Sep 20 '17 at 18:31
  • $\begingroup$ @amWhy Except that Qmechanic explained it in a single comment (If that is what Did refering to because it could mean anything from "Wine" to "Wiskey"). I am not saying to write a one page answer, I am just saying he should write $W = \left|x-\ 2\right|\ -\ \left|x\ -\ 3\right|\ +\ \left|x-4\right|$, he could use >! if he wants. $\endgroup$ – A---B Sep 21 '17 at 14:33
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    $\begingroup$ @amWhy It is reasonable to think on an answer that one does not understand if that answer include some mathematical trick or insight which is not obivous. Why should I be thinking on a answer that is vague and incomplete just for the sake writing one word answer ? It is just trying to be a smartass in this case. $\endgroup$ – A---B Sep 21 '17 at 14:44
  • $\begingroup$ You might want to take a look at that $\pi = 4$ question again. Do you remember roughly how many votes it had gotten a week ago? It's up to 553 now. $\endgroup$ – Robert Soupe Sep 22 '17 at 15:59
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    $\begingroup$ @RobertSoupe It's gotten two upvotes since September 15; you can see the full post timeline for this. $\endgroup$ – user296602 Sep 22 '17 at 17:13
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    $\begingroup$ @A---B In your objection to the W answer, you are missing an important point about the respective values of symbolic thinking and geometric thinking. Geometric thinking has value too. That one letter W answer is vastly and immediately generalizable to someone who has trained their geometric thinking. $\endgroup$ – Lee Mosher Sep 23 '17 at 16:03
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    $\begingroup$ @LeeMosher I am NOT objecting against the validity of the answer. I just said (s)he should edit the answer to include the equation (s)he is refering to. Writing $W$ without saying what it is refering to is vague and meaningless. And BTW what is the harm in including the equation, if nothing else it will help boneheads like me to understand it ? I know, it would destroy the meaningless gimmick of the answer. Of course we can't destroy that gimmick. $\endgroup$ – A---B Sep 23 '17 at 21:15
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I think most people who upvote don't do it to reward the asker, or to vouch for the quality of the question.

They think, "yes, this is a question that I too would like to see a good answer to", and have some fuzzy idea that upvoting the question will make it more noticed by people who can write good answers to it (or make them more motivated to answer).

In reality, of course, it is quite limited how much upvotes on a question contribute to exposing it to willing answerers -- except when they propel it into the Hot Network Questions list. But it still think it is natural to think that way.

The natural outcome of this effect is that questions get more upvotes the fewer prerequisites there are to wanting to know the answer.

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The problem is that seemingly easy is opinion-based.

I would argue that the question given as example is interesting and not that easy, at least for a relatively large part of the audience of the site:

Interesting for beginners:

  1. It is a key point of most calculus course: proving that $\displaystyle \lim_{x\to 0}\frac{\sin(x)}{x}=1$ is the starting point to prove the differentiability of trigonometric functions. So it is an important question for most beginners in Calculus
  2. One may not be convinced numerically that it is true: it works only if you use radians, which undergraduate students may fail to see.
  3. It cannot be proved by obvious algebraic manipulations like $\displaystyle \lim_{x\to 1}\frac{1-x}{1-x^2}= \frac 1 2$ or other limits of rational functions.
  4. It is a nontrivial application of the Squeeze Theorem, in opposition to the classic "$-1\leqslant \sin(x)\leqslant 1$" use of the Squeeze Theorem.

Interesting for a more mathematically mature audience:

  1. The question is well-research and focused: it explicitly says that the result can be easily obtained by more advanced techniques like power series, but asks for a more elementary methods. I am sure it got upvotes from an advanced audience because the question makes you "review your classics".
  2. It got great answers with great figures. The answers illustrates the link between angles in radians and arc length...

I know that the point of this meta-question was not on $\displaystyle \lim_{x\to 0}\frac{\sin(x)}{x}=1$ in particular, but the arguments above apply to most "highly upvoted seemingly easy" questions.

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Some questions get large numbers of views (and consequently large numbers of votes) because they are mentioned in popular places outside MSE.

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