It does work like that to some extent, since closing as a duplicate require a certain number of votes. But this could probably be improved as per the suggestion, as it seems many people have experienced inappropriate "closed as duplicate". It seems to be one of the major complaints in this thread.
Sometimes the duplicate is blatant, but in many case it is really a judgment call. In my experience I more often vote for "reopen" than for "close", so there are definitely different attitudes to what is considered a duplicate.
Alternatively, it could be the decision of the one asking the question. Just as they select the "accepted" answer, they could choose to accept or reject the duplicate as appropriate.
Sometimes the duplicate is blatant, but in many case it is really a judgment call. In my experience I more often vote for "reopen" than for "close", so there are definitely different attitudes to what is considered a duplicate.
Alternatively, it could be the decision of the one asking the question. Just as they select the "accepted" answer, they could choose to accept or reject the duplicate as appropriate.