It's not as if it all begins and ends with the jury. Lawyers present the case, and are tasked with provided evidence for both sides of the argument. The jury then votes - for high crimes their determination must be unanimous. The punishment then falls to the judge, and the carrying out then to the prison system.

As for who leads us, that's a loaded question. In my world alone there are hundreds of countries each with their own methods. From monarchies to democracies to dictatorships.