> At this point, we can just randomly pick a citizen to be President or PM. We might have better chances that way

I have a wild idea. What if we try to select people based on their respective expertise in an area, rather than based on just popularity? If they have a science/knowledge background, even better.

Since it's based on skill and governance, we can call it something like "tekhne kratos", taking inspiration from the Greeks because why not.