This is not a question about the who but rather the how. As such it is NOT a duplicate of those questions marked as possible duplicates. Please read on:
This seems to happen a lot (to me anyway, maybe it's just bad luck):
When answering questions for new users they often don't know how to accept answers. Often a new user comments under an answer with something to the effect of 'thanks, this sorted out my problem' then promptly ignores any attempt to inform them that there is a mechanism for formerly accepting answers.
Currently there is no mechanism for converting such comments to actual acceptance even though the intention of the questioner is completely clear. Right now it's just left up to the community to upvote. This sometimes doesn't happen for even officially accepted answers so I think the situation has room for improvement.
In short I am addressing the problem that there is often no reward at all for answering questions for new users. This lowers the incentive to do so.
There are two possible kinds of solutions to this. I will detail each below. I will be happy to hear of any alternative approaches to solving this problem besides these.
I don't believe that this specific situation has been detailed before in a question here (I searched and couldn't find anything quite like my question. The questions listed as duplicates are are very general in comparison or just different). For them what down vote: Please answer this question as a comment or something, I am very interested to know: do you disagree that the current situation is sub-optimum? Or do you disagree on the suggestion that the obvious intension of the questioner should be honored?
Possible Solution 1: Making the current mechanism more obvious
I, as well as certain others, have taken as leaving this here as a comment on new user's first questions:
This comment tends to get upvoted so I think this possible solution will likely be agreeable. So here it is:
Why not include some kind of welcome message or tutorial bubble or default first comment on all questions until the questioner has accepted their first answer?
Naturally we wouldn't want the thing to be annoying but it should clearly illustrate the mechanism of acceptance.
For example a comment like this may be appropriate for new members:
"welcome to StackOverflow. If you are unfamiliar with this site pretty please click here to see how to officially accept an answer to your question. It would be a great way to say thank you to anyone that lends a hand to you here"
So what do you think? The comment can then be automatically removed as redundant once the user accepts their first answer, and can be pasted onto each of their questions until then.
Possible Solution 2: Add a new mechanism for accepting answers
I know that suggesting that anyone but the questioner gets to tick a question is considered very naughty but, I urge you to ask yourselves why. And to read this before deciding it's such a bad idea.
If a user says 'I accept your answer' their intention is clear, yes? Also it is clear that they don't know they can green the tick to mark something as correct, or don't know the value of doing so. These facts are undeniable and totally totally obvious.
So why can't such comments me considered a mechanism for acceptance? Allowing some high-ranking joe (or a collection thereof) to vote a flagged comment as 'equivalent to acceptance' does not seem particularly harmful to me.
If this would in any way be harmful please please explain why. I have read explanations of why community acceptance of answers is a bad idea and how the very notion is made redundant by the voting process (and i agree), but this seems a little different since the intention of the questioner is crystal clear, ant it's that intention that matters the most.
Since answers can be marked as not correct after all I fail to see the danger in this.
The fact is that many correct answers are only unofficially accepted as correct. This situation is not ideal. I have made some suggestions about how to rectify the situation. These suggestions may or may not be seen as worthy but I am sure that there is some generally agreeable way to address this. So let's put on our thinking caps and address this. Why not?