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In the last couple years I have asked just a few questions on Mathematics Stackexchange and Physics Stackexchange. Recently I have become much more active. I now spend considerable time on Mathematics Stackexchange, writing (hopefully worthwhile) contributions in response to questions of students. As a theoretical physicist I have a very pragmatic "hands on" approach towards mathematics. I think a "keep it simple" attitude is a skill students should acquire.

Now as I began contributing my answers, I also became involved in the reward/reputation scheme which permeates this site. And initially I thought it was a positive thing, and even kind of amusing, that I scored +1 point with a lengthy reply. Yihoo, I scored a point !

However, I soon realized that strange things are happening. A student asks a very basic question. An expert gives a very technical reply, way too complicated for the student to understand. In practical terms, the reply is almost useless. However the expert reply is immediately up-voted, and may receive 10, or 20 or even 50 points. While a (in my humble opinion) much better reply, directed at the student's level, is rewarded with zero points.

It also happens a lot that an expert jumps in with a one-liner. E.g. a question about complex number theory. Reply: "Use De Moivre." Or "Just set exp(ix) = cos(x) + i * sin(x)." Brilliant reply! Scores 10 points. For zero effort. Whereas a much more thorough reply is simply ignored.

I believe that the main purpose of the reward system is to encourage people to participate, to write good answers to mathematics questions. However, I am now at the point that I question the fairness of the system. Actually it is rather annoying to score +1 for a good reply, when you know that others receive +10 more or less for free.

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    $\begingroup$ This is a fair post in my opinion. I agree with your observation, and unfortunately it would seem that such a large portion of users treat the site as though it is a homework deposit, and these same users have voting abilities. Also, in my opinion this is unavoidable(and is entirely democratic). $\endgroup$ – user142198 Nov 22 '14 at 9:08
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    $\begingroup$ A large factor you have missed: You don't use $\LaTeX$ in your posts. This is likely a very important factor in voting decision. $\endgroup$ – user142198 Nov 22 '14 at 9:16
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    $\begingroup$ There is no reason that a completely decentralized voting system will lead to an outcome that agrees with some standard of fairness. But please keep in mind that answers her are not just for the person who asked and that is why everything is public. Many people can learn something valuable from an answer that is of less use to the person asking. $\endgroup$ – Michael Greinecker Nov 22 '14 at 9:16
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    $\begingroup$ I just glanced over your answer history... Using mathjax would be a good start. And maybe I'm confused, but in almost every case where you weren't upvoted as much as the other answer, the other answer was much, much more detailed (at least over your last 20 answers). Which conflicts with your idea that good, detailed replies are ignored over one-liners (I'm not saying it never happens, but...). $\endgroup$ – Najib Idrissi Nov 22 '14 at 9:17
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    $\begingroup$ And I disagree that a one-liner requires zero effort. Typically when I want to give a hint to a question, I do my best to give one that (a) will help the asker find the answer but (b) not chew all the work for them. There's a fine line between an incomprehensible hint and one that solves directly the problem. And if the question can be solved in one line, why not? $\endgroup$ – Najib Idrissi Nov 22 '14 at 9:21
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    $\begingroup$ I don't know when was the last time you've had students. But the ability to give a good hint, that will set a confused student right on the path towards a solution is not a trivial ability to develop. I agree that not all one-line answers are good, many of them are bad simply because there are so many of them. But giving the correct perspective on a problem, without solving it completely for the OP, can be incredibly tricky. And that deserves reward, much like the ability to write a full, detailed and pedagogical answer. $\endgroup$ – Asaf Karagila Nov 22 '14 at 9:59
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    $\begingroup$ Regardless of the arguments towards the OP's views, it's undeniable that the higher reputation a user has, the easier it is for people to up vote him on rep. alone ( and blindly so). $\endgroup$ – Git Gud Nov 22 '14 at 11:56
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    $\begingroup$ I have a question for you: How come after 23 questions and 2 answers you still haven't voted on a single post? $\endgroup$ – Thomas Nov 22 '14 at 12:53
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    $\begingroup$ A related question. $\endgroup$ – Lucian Nov 23 '14 at 1:58
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    $\begingroup$ @Thomas 23 answers, 3 questions. $\endgroup$ – apnorton Nov 23 '14 at 3:18
  • $\begingroup$ Once in a while short, worthless answers do get downvoted like they should. Earlier today someone asked something about the last two digits of a sum of powers always being 54. One answer was "HINT : Use Principle of Mathematical Induction." It did score him 10 points, but then it scored him $-8$ points. The system works. $\endgroup$ – Robert Soupe Nov 26 '14 at 1:57
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    $\begingroup$ It would be nice if everyone tried their best to be generous upvoters (questions and answers). $\endgroup$ – JohnD Nov 27 '14 at 23:05
  • $\begingroup$ It’s a form of democracy, but, as of fairness, a total failure for several reasons. Two most important are: unfairly high reward for questions (although has more to do with voting habits, not technology) and anonymity. Also, forget about physics.SE just now: what happens there has nothing to do with scientific peer review. $\endgroup$ – Incnis Mrsi Nov 30 '14 at 16:24
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    $\begingroup$ @Committing to a challenge and 17 upvoters of 2nd comment: can you look at meta.math.stackexchange.com/questions/17496/… ? $\endgroup$ – Incnis Mrsi Nov 30 '14 at 18:44
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    $\begingroup$ @JohnD: I don't want upvoting to be generous -- I want upvoting to correlate more strongly with "I thought this post was good" than "I saw this post". $\endgroup$ – user14972 Dec 3 '14 at 21:52
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You ask how democratic and fair the reputation system is. I will start by answering that "democratic" and "fair" are not the same thing. This site allows just about anyone to come in and upvote, and not too many fewer to downvote. Allowing just about anyone to vote, while highly democratic, leads to results that may be far from "fair," depending on your sense of that word.

So, while I think all of us can agree that the current system is democratic as far as we understand what democratic is (i.e., near universal participation), how fair is it really? Quite fair!

You have to remember, for every question and corresponding set of answers, there are two considerations:

1) # net votes from the community

2) acceptance by the OP

1) is a measure of how useful an answer is to the community. The reason votes are important is because every answer is visible to the community as a whole. It is searchable, so that when someone needs that answer, it is there. And having the endorsement of the community should imply that the community thought it a very useful answer to the question to which it corresponds.

2) is a measure of how useful an answer is to the OP who asked the question in the first place. Thus, having two separate measures is an acknowledgment that the needs of the OP and those of the community do not always match up. (Frequently, the OP will accept an answer that gets fewer upvotes than others.)

Is this perfect? No! Democracy allows non experts to vote, and they may make bad voting choices. There is a penalty for downvoting, so many people are reluctant to downvote bad answers. Sometimes, as software developers know all too well, the OP has no idea what (s)he wants and accepts an awful answer that reinforces existing prejudices. Another problem may be a built-in bias toward answers from folks with high rep - although I wonder how much of a problem it really is, even if demonstrably true. (Folks need to earn their respect, and those who have consistently provided high quality answers get the benefit of the doubt. Real life works this way.)

That said, it is the best system we have for the purposes of SE: to have a participatory, living knowledge base that draws users to the best questions and answers. In the large, this system works extremely well. Anyone with a math question that knows how to ask it will likely find a very useful answer here.

I took a look at some of your answers to understand the nature of your complaint. The first thing that came to mind is that you need to adopt MathJax: maybe there are useful ideas in those answers, but they are hard to read. (You also come off as uninterested in whether your stuff actually gets read.) I for one will not upvote an answer that requires too much work on my part to translate. (Going through complex math is not work in this sense!)

The second is that sometimes all that is required is a brief answer. Brevity is a virtue, always!! Just because you write a novella does not win you the right to upvotes. Your prose must be readable, and to do that you must draw people in.

Let us consider this answer, for which you got zero votes. (The only other answer got 1. I see you did use MathJax here.) The OP asked a general question couched in a specific example: why do we have to consider branch cuts when computing "this kind of integral" with a square root? In my opinion, the OP was not really asking for the result of evaluating the integral he posted. Rather, he wanted to know why branch cuts were necessary in certain integrals and what effect they have on their evaluation. Your reply was correct insofar as one would evaluate the integral: sometimes you can get rid of branch cuts altogether by substitution. This is very true, but unfortunately it is not useful. The real question was about how to deal with branch cuts in integrals to be evaluated via complex analysis methods. The OP could have used a better example, as there are many in which one cannot easily get rid of multivaluedness, and therefore has to address the choice of a branch cut. So you didn't answer the question. That said, was your answer useful to the larger community? There, I'd also have to say no because your answer will not be found in a search of evaluating integrals with multivalued integrands.

Another one of your answers stands out to me. Here, not only do you not use MathJax, but you close with the line "[l]ater on in the evaluation setting y = sin(t) may well be a promising idea." (Emphasis mine.) Again, you received zero upvotes. In this case, the system worked because stating that something "may be promising" is not a useful answer, ever. Either you've done the problem or you haven't. Guessing along some line without having traveled down that road is not only not useful, but in many cases harmful. I actually would have expected to see downvotes, but zero works too.

My advice if you want to reap the rewards of the system better:

1) Use MathJax.

2) Read the question carefully.

3) Provide a brief, readable answer that completely provides what the OP asks.

4) Don't guess.

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    $\begingroup$ This comment isn't arguing against anything in this answer. "Your reply was correct insofar as one would evaluate the integral: sometimes you can get rid of branch cuts altogether by substitution. This is very true, but unfortunately it is not useful. The real question was about how to deal with branch cuts in integrals to be evaluated via complex analysis methods". There are many, many instances in which people just solve the given problem instead of answering the actual question and get all the votes and sometimes even the acceptance! $\endgroup$ – Git Gud Nov 22 '14 at 12:06
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    $\begingroup$ @GitGud: Of course. But the OP is asking why he is getting no respect and how to get better responses to his answers. He has a better chance addressing the question than by answering something else. $\endgroup$ – Ron Gordon Nov 22 '14 at 12:08
  • $\begingroup$ Re: your comment about the branch-cut. Your interpretation would be correct if the OP had formulated his question as follows. "I am currently studying complex function theory and in particular contour integration. I am aware that sometimes branch-cuts are required. I would like to understand how this works. Consider the following integral, which has sqr(x) in the numerator. What is the best place for the branch-cut, and how I should I proceed?". But this is not at all how the question was formulated!!! $\endgroup$ – M. Wind Nov 22 '14 at 21:42
  • $\begingroup$ Re: your comment about a post of mine that ends with "may be promising". User Venus posted a very challenging integral. She herself invested hours in solving it, without result. And none of the math experts here was able to solve it. I spent a lot of time on it, and came up with a substitution which cleans up the denominator considerably. And yes, I suggested that later on a second substitution of the sin(t) type might be necessary. Was that wrong? Many experts make similar suggestions using the term: "HINT". They are usually rewarded for it...... $\endgroup$ – M. Wind Nov 22 '14 at 21:46
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    $\begingroup$ @M.Wind The difference is that the people who write "HINT" are implying that either 1) they've worked out the problem and know first-hand that the hint is useful, or 2) they've worked enough problems to know that it is applicable. That is, saying "HINT" isn't saying "this may be useful," but rather saying "this will be useful." Therein lies the difference. $\endgroup$ – apnorton Nov 23 '14 at 3:21
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    $\begingroup$ @M.Wind the question doesn't have to be formulated as you said. The question has already the relevant tags, and the answerers should pay attention on tags set on the questions to address them in the right scope. $\endgroup$ – Ruslan Nov 23 '14 at 17:03
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    $\begingroup$ @M.Wind: Look, I am just a messenger. If you think I am wrong, then so be it. Keep doing what you're doing and assume that there's some cosmic injustice going on here. That'll get you far. $\endgroup$ – Ron Gordon Nov 23 '14 at 22:23
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Well, at some level, the system works regardless of whether it does what it says on the label. The users with a lot of reputation tend to post well-written answers, and do so in good faith. Of course, at some level, this is probably because if someone has high reputation, it means they've invested a lot of time in the site, and if they've invested a lot of time in the site, they probably enjoy it for its own sake, and aren't looking to get "free" reputation. This hypothesis doesn't require anything except that reputation measures activity.

However, I think reputation does work better than that. A user who writes good answers will more quickly gain reputation than one who writes bad answers. I certainly feel that for some given question, in general, the highest voted answers are more valuable than the lower voted ones. This doesn't mean that it is always the case, but that it probably averages out. Yes, sometimes an answer that receives many upvotes is not necessarily helpful to the OP, but it represents the same effort towards the question - and if the OP desired a simple answer, they ought to have specified what theorem's they're trying to work from or what their previous attempts have been (and it is absolutely their responsibility. That's much of the reason why "missing context" is a valid reason to close a question - it's harder to give a useful answer to a question that looks like it came off a sheet of homework).

Moreover, answers which address an OP's specific, stated concerns tend to receive more upvotes than those that don't. For instance, in proof-verification questions, there tend to be lots of answers which provide a different proof of the desired property, but I don't often see these upvoted (and even less so accepted). In these questions, the highest upvoted answers tend to address the particular reasons why the OP's proof fails (and to repair it if possible) - and when they don't, the failure of the proof is often addressed in the comments to the question already, so the OP will get that value out of it.

So, if we're being sure of it, the reputation one answer receives relative to another (on the same question) measures "How well does this answer address the question?" and not so much how helpful it might be to the OP. There's a lot of randomness in the system for sure, since the set of people who see each answer varies wildly between questions, but the system has enough bias in the right direction that things seem to work out okay in the end - and that's all that's really necessary since, when you have even a couple thousand points, a single upvote is appreciated more for "Yay, someone read and liked my answer!" than for the points it gives, since points hardly mean anything else by then.

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This isn't a full answer, but I think it belongs here rather than in a comment. I just want to mention a specific flaw that I think exists.

I think that for basic-level questions, the system rewards quick answers.

The impression I get is that most of the voting happens very shortly after the question is posted. But a good answer is likely to take a bit longer: for example How do I not just answer this basic question, but communicate the basic concepts that the questioner hasn't grasped, in a way that they will understand? By the time that answer is posted, everyone's lost interest in the question and one of the answers posted in the first ten minutes has lots of upvotes . . .

I'm not sure whether this is unfair to individuals, since it won't necessarily be the same people posting quick or slow answers every time, but I think it's unfair to the answers, in that they can end up being ranked in order of "superficially-best quick answer" rather than true usefulness to the questioner and the site.

I also think that a good answer is sometimes the result of someone feeling that the existing answers aren't quite adequate and wanting to post something better.

Maybe there should be a time delay (say $30$ minutes or an hour) between a question being posted and it being possible to vote on the answers.

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    $\begingroup$ Ah, that's an interesting suggestion, to impose a waiting period not on the posting of answers but on the voting. $\endgroup$ – Andrés E. Caicedo Feb 24 at 1:09
  • $\begingroup$ I've noticed the issue mentioned by @timtfj myself quite a few times, & have thought about what, if anything, to do about it. Instead of delaying the ability to vote for a while, like $30$ minutes or an hour, I thought of having the amount of reputation awarded being a bit less, like only $8$ or $9$ instead of the normal $10$. As for the opposite issue, answers which are provided considerably later, like a day, week or even over a month later, perhaps up votes for them can be a bit more, such as $15$ or so. I'm not sure what's best to do, plus we need to be careful of unintended consequences. $\endgroup$ – John Omielan Feb 24 at 3:25
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I think that a less democratic voting system could be more fair. Say that you need a reputation of 100 points to vote and that your vote then is worth 1 point and that for each 100 points your vote will be worth additionally 1 point up to a reputation of 5000 points and a maximum of 50 points per vote $-$ then the questions and the answers would be more accurate judged. Under the premise that higher reputation means greater sense of responsibility, especially with increased power!

But personally I like democratic imperfection, since it brings tension and struggle into the process and a sound perspective to point hunting.

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    $\begingroup$ I think there's a fine balance to be struck on such issues; we want to bias the system in favor of established users - such that they may maintain the community norms - but ultimately govern the site by the masses. The current system - where getting to downvote is far from immediate and other moderation things open up considerably later - seems to accomplish this fine. Also, there's no guarantee (or need) that each post will be read by high rep users. $\endgroup$ – Milo Brandt Dec 10 '14 at 4:13
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    $\begingroup$ "Under the premise that higher reputation means greater sense of responsibility" Higher reputation generally means greater amount of free time on your hands. $\endgroup$ – Gerry Myerson Dec 10 '14 at 4:50
  • $\begingroup$ @Meelo: I agree, but if high reputation was better correlated with skill, also high scores would be better correlated with accurate posts. But the system is more attractive as it is. $\endgroup$ – Lehs Dec 10 '14 at 11:48
  • $\begingroup$ @Gerry Myerson: You are right, but if it was harder to get high reputation this would shows in accurate voting scores. But the system is nice and shortcomings are natural. $\endgroup$ – Lehs Dec 10 '14 at 11:53

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