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Preventing people from asking a question that has already been asked is pretty difficult actually. The best option I can think of right now would be to incentivize people to post something like "This question has already been answered at URL", and then have a moderator merge the two questions. Or something like that. I cannot think of a solution that would not require a lot of manual labor from either the users or the moderators. 

I don’t see this as a major problem. Yes, musers should do their part and search for similar questions before asking. But some questions do deserve a second asking, especially when there aren’t enough or satisfactory answers given before.

I used Quora a lot and had seen repetitive questions being asked. However, as the topic interests me, I don’t mind reading new answers to it. You will always find better answers given in a different perspective. I find that beneficial for the platform.

Instead, I would suggest musers not to post too many questions a day, in the hope of earning upvotes. Some questions that I came across are really unworthy for this platform. A simple 1 minute search on google is enough to get the answer, but yet they prefer to ask it here. What a waste of our time and resource.

Probably nothing, apart improve the categories and the search experience

One thing I could think of is to add a "relevant questions" list below or side the main question. This will let users and musing curators know that the question was already asked before.

They could further improve this one to, letting musing curators or moderators hide repeated questions visually or through UI.