This is counterproductive to the goals of Stack Overflow. If you look at other gamification strategies on the site, such as the reputation system and badges, you'll notice that they're carefully crafted in such a manner that desired behaviors are encouraged and rewarded while undesired behaviors are discouraged.
We don't want to necessarily discourage duplicates, since it helps improve SEO and expands the possible keywords that can lead to an answer, but we don't necessarily want to encourage duplicates either, as this is something that could be massively abused and easily get out of hand.
The first step before posting a question is to search, search, search, and if you happen to find the answer to your question, then great. Problem solved! But if not, or if the existing answers don't really fit your situation, then ask away.
However, we don't want a carrot hanging at the end of a stick that's going to encourage people to post without searching. This would be detrimental to a site as large as Stack Overflow and would clutter it up with a lot of useless, exact duplicates that have no value. If a question and its answers are great, they'll get upvoted, and linking them as duplicates actually increases the chances that a user landing on post A may go to post B if the answers on post A don't solve his or her problem.
Additionally, votes are the voice of the community, and artificially increasing votes on a post don't reflect the opinion of the community. I believe this is what Sha Wiz Dow Ard was alluding to in the comments.