My only objection to this is with Approval Voting you don't need primaries. With Approval Voting you can have multiple candidates from the same party in the general election without worrying about vote splitting. Primaries only serve to drag out the election process, requiring greater amounts of money to be spent on media buys to benefit bloated old media, and discouraging people from voting because the process is dragged out. It also steals time from governments that could be spent governing instead of campaigning