Q:

Should there be an incentive for accepting an answer to a posted question?

On this site there are a lot of questions and a lot of answers.
There is an incentive to post a correct answer, but very frequently no answer is accepted as being correct.
By default the most up-voted answer rises to the top, but often there are just several answers, none of which are marked correct.
This has probably been discussed previously, but it seems to me there should be an incentive (reputation / badge etc) for accepting a posted answer as correct.

A:

There already is an incentive to accept an answer:
2 Points for the asker, 15 for the answerer.
But the acceptance does not mean "this is the correct answer", but "the OP liked this one best".
Also, a question does not need an accepted answer to be useful, being a good sign-post for a duplicate or having a good answer is completely sufficient, preferably well-upvoted.
You can help by finding (and flagging, you need 3K to vote for closing) duplicates, by providing that answer where it's missing, as well as by upvoting good answers.

