So what gives? In articles like the one I wrote on the Hagel filibuster, the short explanation we give is that Reid voted no "for procedural reasons" or because a no vote "allows him to bring another cloture vote in the future." But why does it do that? Why is the majority leader required to vote no if a bill is to be taken up again after a failed cloture vote?
As Sarah Binder, a Senate rules expert at George Washington University, told me, it's not that the majority leader has to vote no. It's that somebody on the winning side of the cloture vote — in this case, the side voting against cloture — has to file a "motion to reconsider" if the matter is to be taken up again. "I suppose the broader parliamentary principle here is that it would be somewhat unfair to give someone on the losing side of a question a second bite at the apple," Binder explains. So the rules provide for senators whose opinion has changed to motion for another vote, whereas those whose opinion stays the same don't get to keep filing to reconsider.
Reid, and other majority leaders before him, have developed a clever workaround: Just change your vote at the last minute if it looks as though you're going to lose, then move to reconsider. In theory, any supporter of the bill or nomination in question could do the same, but traditionally it's been the majority leader.