There will be various positions in a city, such as a mayor, a commerce/trade advisor, a research advisor, and so on.
Under the current system, every player will have 3 votes that he or she can cast on a candidate or another. For example, a player can cast all the votes on a candidate, or they can share them between two or 3 candidates (on different positions, of course).
Right now, I am still working at implementing the system, hopefully it should be done by the end of the week.
I still liked the shadow government idea though.