The only times in recent history when it wasn't a question of the presidential nominee making the decision were in 1956, when Adlai Stevenson allowed the convention to decide, and 1960, when Lyndon Johnson blackmailed Kennedy into picking him (Kennedy had intended to pick Stuart Symington). At least that is how Seymour Hersh tells the story.
Joe Biden was selected to be the Obama admininistration’s white lawn jockey.