I've seem many questions by people with a 4% accept rate that have good, upvoted answers, but no accepted answer. Should the public be able to vote on a best answer if the asker has not accepted an answer within an amount of time (a week, perhaps)?
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The public is already able to vote on what it feels is the best answer. They do this by voting on answers.
Most people will take the time to look at the most upvoted answer besides the accepted answer, so it isn't really like the information contained in it is irretrievably obscured to the public eye.