Listen to oliver2002 "there are procedures on how to handle oversold situations. The actual practice varies widely"-- he is exactly right.
If an agent has the time, knowledge, and interest in following procedures, op ups are done by status and, within status groups, by fare class. But getting the flight out on time will trump those procedures.
My manager has no LH status and was on the BOS-FRA flight on the day before the US Thanksgiving holiday in November. She was flying with her family on a low booking class economy fare, was among the last passengers to check in, and the check-in was hectic as the flight was apparently oversold. The agent gave her a BP for 11B, and the rest of her family got economy. (She was a bit disappointed on her return when I told her that she'd only been upgraded to business, not first.)