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This is something I've experienced several times, but it was brought home to me most clearly by my most recent question: How can I best deal with the effects of markers with differing levels of generosity in grading student papers?. At present there are two answers that are quite different from one another, and another answer in the comments that is different from either of those two.

My first step is to apply my knowledge as best I can to the answers and try to decide based on that. If that fails I'll often go with the heuristics such as the number of upvotes an answer has received, or whether the answerer is a user I know to be highly reliable.

However, in the absence of those cues, and with a bounty ticking away, I'm unsure how to proceed. Does anyone have any advice?

Relatedly, is there any way for me to see which users have upvoted a particular answer? If so, that could provide another useful cue.

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    $\begingroup$ You can't see people's votes. The answer in comments is easily dealt with - you can't accept that one, reducing your choice to two. Ultimately the one that solves your problem best is a good one - try the approaches; one might be easier or better. If you're keen to recognize both, it is possible to accept one and award the bounty to the other. It's also possible to award a second (larger) bounty if there are two answers you want to give a bounty on. But it's early days yet - as the bounty period goes toward the deadline, you might have the conundrum reduced by getting another answer or two. $\endgroup$
    – Glen_b
    Nov 17, 2014 at 0:09
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    $\begingroup$ If you want to accept the comment as an answer, encourage the person who posted to expand it to an answer. Often people just post briefly for all the usual reasons, say that they are busy at the moment or just feel that a simple point can be made concisely. Yet that simple point can sometimes unlock the problem for the questioner. $\endgroup$
    – Nick Cox
    Nov 17, 2014 at 0:12
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    $\begingroup$ Thanks, I'll do that. I thought the idea mentioned in the comments seemed rather good, though I can't be sure that I'd accept it as an answer if/when it's written out in full form. $\endgroup$ Nov 17, 2014 at 0:40

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If you cannot decide among answers because it is unclear whether one (or any of them) is correct, then those answers are not good enough for you. You don't have to award them bounties, acceptances, or even your (up)vote. What you should do instead is write comments asking for clarification. Then you can decide on a best answer (if indeed any answer at all is valid) based on objective, rational criteria.

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Your acceptance is yours. No one is telling you how to apply it. You can use it to flag the post you find most useful or helpful, or to flag using any other criterion. If you want to be guided by the community and follow the voting, that is your choice too.

Here's another thing that's important. Sometimes an answer looks better at first than it does after comments pointing out its limitations or even errors. Or sometimes a really good answer arrives late. It's fine for you to change your mind. There won't be flak. It's your privilege.

Remember also that upvotes and positive comments remain other ways of acknowledging good answers even if you don't accept them.

Reputation is a funny thing any way. Even people with moderate or high reputation are often puzzled by patterns of voting: what they think are good answers sometimes are not accepted, or much upvoted, and the opposite happens. So, accepting a question is your way of saying thanks, and thanks for the thanks, but on the whole people here don't take reputation more seriously than it deserves.

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    $\begingroup$ +1 ... the way votes (and acceptances) go often puzzles me, certainly. There's little point getting much invested in such things, except so far as it encourages or discourages good answers more generally. $\endgroup$
    – Glen_b
    Nov 17, 2014 at 0:15
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It's a tricky problem - how does a non-expert choose what's a good answer (if you knew enough to tell reliably, you probably wouldn't need to ask, right?)

I agree that seeing what more knowledgeable people think would help in figuring out which might be better, but there are very good reasons why we shouldn't see who votes for what.

Sometimes two very different answers can both be reasonable approaches to a problem. If it's not clear whether or not they're both reasonable, you might ask for some clarification. Or you could try them, and then ask about what issues you run into when you do.

There's several days in which people can point out problems -- if an answer on a bounty question has a glaring error, it's unlikely to be there for long without someone saying something, so at the end of the full week, you're likely to be choosing between reasonable answers. Let the time run, you may find the choice becomes clearer over time.

In the end, choosing what seems to you like a good answer to your problem (taking into account the various things you already seem to be considering) isn't a bad approach. An answer that speaks to you more clearly is at least exhibiting some characteristics of what makes a good answer, even if it isn't the one that someone with more expertise might choose.

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As the OP, you have no obligation to decide what is the "best answer". After all "best" needs a definition. What should matter to you is select an answer that is useful to you: You may receive a highly sophisticated answer, totally correct, insightful, brilliant etc etc etc. It may be an answer to admire -but it also may be partly or wholly incomprehensible to you, which in all will make it

a) useful in general as an on-line repository of knowledge
but
b) useless to you, for your immediate concern.

In such a case, I would suggest to let the upvoting of the community reflect the answer's "quality and value", but keep your green mark and your bounty for an answer that you can actually understand and use, and not just admire. In this virtual market, the OP is the customer and the answerer are the suppliers: if what you need is bread and I provide a sophisticated French plate, my offering is high-quality, and of higher value than a bread-answer (I love bread, by the way), but it is not certain that it will go well with your stomach. After all, an efficient supplier is a supplier who understands what the customer can digest, otherwise he risks turning himself into a participant in a beauty contest.

@Glen_b's suggestion that the green mark and the bounty need not necessarily go to the same answer, is also a good policy advice, IMO.

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