Suppose that a user does not genuinely accept the best answers on their questions, but instead accepts all the answers with the fewest upvotes. I appreciate the fact that everyone is free to choose his/her votes and accepts, but that would seem like plain trolling to me. People who spent their time throughly answering questions should get appreciation from the community for that, but the user isn't using the system like they are supposed to. Should something be done?
I would say that we shouldn't do anything - a user is indeed entitled to accept the answers they want. Whether or not one's answer is accepted is of relatively little consequence, anyway: the reputation gain from having an answer accepted is +15, while a genuinely better answer will get more upvotes, which give +10 each, so already an answer with 2 more upvotes than the accepted answer will give more reputation. But if the fact that a user doesn't accept the "actual" best answers causes the people who provide the "actual" best answers to avoid answering that user's questions, that will only hurt the user themself in the long run.