What role does shame, as Confucius terms it, play in motivating behavior? What does it have to do with running a city, or a country?

Shame motivates behavior in more ways than one. Shame can cause you to act with extreme power, or act in harsh ways, or sometimes in a more charitable way. It motivates you to use behavior that covers up an act that brought on the feeling of shame in the first place. If you are shameful, you can not run a city or country effectively, because you are not in a stable mindset if you let that shame effect your actions in negative ways. If you deal with your shame, for example: by accepting the mistake that caused you to feel shame, then learning from that mistake and knowing how to avoid making it again.