When an OSPF router becomes active and discovers its neighbors, it checks for an active DR and BDR. If a DR and BDR exist, the router accept them. If there is no BDR, an election is held in which the router with the highest priority becomes the BDR. If there is no active DR, the BDR is promoted to DR and a new election is held for the BDR.
It should be noted taht the priority can influence an election, but will not override an active DR or BDR. If there are already DR and BDR on the LAN, they will remain DR and BDR until a failure.