The thing that makes real-life politics interesting is the balancing of powers. The carefully crafted constitutional checks and balances among the legislative, executive, and judicial branches of the U.S. government is one example, but pretty much any public organizational structure will pit one power base against another. In some of today's nations there is a tension between religious and secular leadership. Even dictatorships often split into civilian and military power blocs.
MMORPGs that offer player cities and that want to stimulate (if not simulate) player politics need a way to create power blocs within city administrations.
Some games such as SWG have made a reasonable start at achieving this by letting players be citizens of player cities, and by allowing players to become Mayors of those cities. EVE Online has a more abstract version of this in which players can be members or CEOs of corporations.
These are good starts, but they don't go far enough to really provoke political intrigue. For that, a middle layer is necessary -- there needs to be a power group between the leader and the citizens. Only when multiple players are able to compete or cooperate to define and execute rules do you really see the kinds of interactions that make politics so interesting. (An example of this would be king, aristocracy, and bourgeoisie. Shifing alliances among these three groups generated a much more diverse and interesting politics than the more direct command-and-control system of a ruler and the ruled.)
Here's how this three-group system might work in a MMORPG. To use the analogy of a city, I'd like to see players able to win seats on a City Council. Novice politicians could earn political points serving as an executive assistant, or legislative staffer, or some such thing. Once you earn enough political points to learn a City Council skill, you can run for city council. (Council races would occur weekly, mayoral races would be held independently once per month.) Election to the city council would give you the ability (depending on the skill level) to do certain legislative things -- basically changing certain existing laws and sponsoring new ones, each of which would generate political points. The city council would vote on these "bills," which if agreed to would go to the Mayor for signature or veto. If vetoed, the council would have a chance (through another vote) to override the veto.
This restructuring of the power system would have a number of positive effects on gameplay. It would allow more people to be able to actively serve as politicians, rather than only allowing one person to be Mayor. It establish a tension between the executive (Mayor) and legislative (Council) power structures -- the city council itself could become a political battlefield on some issues. It could even set up "insider" vs. "outsider" dynamics, as between someone who's sat on the city council for months ("I know this town, and I know its citizens") versus someone who's never held public office ("I've got fresh perspectives, and I'm not beholden to any pressure group").
Something similar could work for corporations. Holders of enough shares or proxies could constitute a control board overseeing the actions of the corp's CEO.
Overall, I think the simple citizen/Mayor system concentrates too much power in the hands of one person. It's not a matter of fearing the corruption of power -- it's more that politics isn't as much fun if only one person can play.
We need checks and balances. And babies to kiss!