This is how I understand the discussion at hand:
"The question poster posts a question. After some time several answers have been posted but the question poster haven't ticked any answer as "the accepted answer"."
You suggest that this should be be fixed by introducing a voting period after which "the accepted answer" becomes the most voted one.
Such a feature is almost already in place if you after 2 days choose to place a bounty on your question. If no answer is selected in 7 days the most voted becomes "the accepted answer" and it's impossible to change that later.
Problems might arise since all of the following aren't true:
A. Every question can be answered by the people on the site. No -> Some questions on this site right now are without a good answer.
B. Every question can be answered within a time-frame. No -> Obviously not since there are questions still not answered.
C. Every question can be answered within a number of posts. No -> This is not true since 100 answers can be 100 bad answers. Especially with unconfirmed rumours that a community leans on without proof.
D. Maybe a specific number of votes for one answer makes it a good answer. No -> Maybe people voted on it because they had not seen the real answer to the question. Suddenly the real answer is posted. Well aren't we screwed. Also sometimes a post have a lot of votes without having answered the question fully or just a little bit. It's the best there is and therefore it receives votes. Do the question really then have to have an "accepted answer"-tick until a good and full answer is posted?
E. Every top-answer posted is the full and complete answer. No -> Sometimes an answer is made up of posts from several posters.
A question can be auto-selected as the "accepted answer" if the answer has gone over let's say 5 votes and there exists at least 2 other answers posted and seven days have gone since anyone posted an answer or commented or edited the question. The question poster still has the ability to change the "accepted answer" or to remove it completely.
On another matter: you should be able to split an "accepted answer" mark onto several answers (or people should start merging their answers with others).