In situations like this where it clearly won't matter, I've always seen it as basically a token vote that they pass around to whoever's turn it is. Everybody on the team gets a few votes throughout their term where they can vote against something that will pass anyway and then they can turn around later when their constituents are mad about whatever and just say "but remember? I voted against that thing you hated!"
I could of course be completely wrong but it just seems like the math just barely works out in the majority party's favor way too much to be a coincidence.