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?)