After checking MO a bit, it is clear to me that the idea of an "accepted answer" is not well thought. Here is a quick proposal for a possibly slightly better version. Now, I am not sure how difficult is it to change the software, but anyway.
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Allow the possibility of a "partial answer". Give fewer, say, 5 reps for it to the answerer and give 2 reps for the questioner. Require the questioner to write between 100 and 300 letters comment why this is a partial answer - no reps otherwise. Allow maybe 3 partial answers per questions to the questioner and 3 for other MO crowd with over 1,000 reps, but in the latter case make them pay the "partial answer" bounty (extend the comment requirement to them as well). Make only slight color changes in the search for questions with partial answer, or none at all. Keep the "accepted answer" with its 15 reps (also, allow "partial answer" to be upgraded and pay the difference of 10 reps). Again, require a 100 -- 300 letter comment why this answer should be accepted, and give maybe 5 reps to the questioner. Finally, make all such comments "community wiki" so others with sufficiently high rep (say, greater than 400) can edit it.

Yeah, I'm not sure why this would be any better than using comments. It doesn't really matter how the reputation is divvied up -- good answers get votes, and multiple good answers all get votes. The point of "accepting" an answer is just to provide a visual indication that the asker thinks there's a single satisfactory answer to the question, and perhaps a hint that you don't need to read anything else.