Why do we have to accept just one answer? I mean, in some questions there are lots of good answers which deserve to be accepted; why do we have a restriction on the number of accepted answers? I think if we allow accepting more than one answer, we could attract people to answer a question with an accepted answer.
That is what changing your accepted answer is for! Always choose the best answer. If a better answer is posted, accept it.
This isn't really a problem because we want people to answer unanswered questions more than we want them to spend time trying to come up with better answers for already answered and solved questions. (Although that is fine, too; it is just not... economical?)
Multiple accepted answers System
Is accepting an answer discouraging more answers?
21$\begingroup$ I don't agree that "we want people to answer unanswered questions more than we want them to spend time trying to come up with better answers". Much of mathematics was discovered by searching for "better" answers. Alas, the SE platform does not encourage such. Rather, it rewards quicker answers, which are not always higher quality than more thoughtful answers (which usually appear later, requiring more time to compose, and/or because experts visit the site less frequently, etc) $\endgroup$ Jan 2, 2012 at 20:30
1$\begingroup$ I think this is a wrong approach. I agree with @Bill Dubuque. $\endgroup$ Jan 3, 2012 at 11:10
$\begingroup$ @BillDubuque That is the FGITW problem. No one is discouraging the user to search for a 'better' answer and discover some mathemagical thingy on their own, and becoming world famous for it, but the focus of this site is Q&A. This 'solution', however, is awkward, doesn't work, and there are better alternatives (which are also awkward, but not nearly as much as this one). $\endgroup$ Jan 4, 2012 at 2:57
$\begingroup$ @muntoo I explicitly chose not to use the SE lingo since not everyone here knows what it means. I cannot comment on the rest of what you wrote since I have no clue what "this solution" refers to; ditto for "this one". $\endgroup$ Jan 4, 2012 at 2:59
This solution/this one == Accepting more than one answer. Alternative solutions to FGITW include disabling sorting by votes or displaying the number of votes for a set period of time. (Between five minutes and one day, IIRC.) $\endgroup$ Jan 4, 2012 at 3:10
1$\begingroup$ Yes, I read the SE FGITW threads long ago. Part of the problem is the 1-dimensional nature of votes. It would be nice to be able to vote on different aspects, e.g. answers that are best: conceptual, elementary, general, etc. Note: I don't disagree with your first paragraph on changing answers (so I didn't downvote). My point was to simply to raise awareness of other viewpoints on the issues in your 2nd paragraph. $\endgroup$ Jan 4, 2012 at 3:20