In the authority before responsibility model, you are waiting to be picked and blessed as a leader so that you can tell people what to do.
The responsibility before authority model is different. You don't care about being picked by someone to lead. You rally the troops and march towards a shared cause. You are an owner of the cause. You don't need someone to choose you.
Too often in workplaces, I stumble on this scenario where someone either plays the authority card or the lack of. Don't wait to be picked by authority to be an authority. Rather, take responsibility. You pick yourself because you are doing the right thing. Rest does not matter.