Rules for getting bumped from an overbooked flight?

Before online check-ins, I believe that passengers were bumped by the order in which they checked-in at the counter/gate. Does anyone know how airlines determine the order of people getting bumped these days?

This is an automatically-generated Wiki post for this new topic. Any member can edit this post and use it as a summary of the topic’s highlights.

I thought they always made an announcement asking for volunteers and offering compensation.

That’s only because the cost of involuntary bumping a passenger is far more. He’s asking about when there are no volunteers that accept their offer.