I believe the idea is that if you push the button, it goes on to someone else. If they DON’T push the button, they get skipped. It goes to someone else besides them. And so on, until SOMEONE does push the button. And at that point, the last person who pushed the button gets iced.

And so in that way, every person who pushes the button inevitably gets killed, removing selfish people from the world while morally upright people get passed over.