The council's duties, political structure and balance of power can vary city by city. Listed here are some of the more stable and reasonably fair types of primogen counsils.
Strong, Balanced Democratic Council Under a Weak Prince
This is the best arrangement for the primogen, the counsil is democratic and holds power over a weak prince. Typically the primogen will suggest proposal to the prince, the prince will rubber-stamp them, and the primogen will decide the matter through a vote. Primogen on these types of counsils are most likely to keep their clans in check, to keep friction between the prince and clans to a minimum and avoid upsetting the advantageous balance.
Strong Counsil, Balanced in Favor of a Bloc
This model is similar to the first, only a bloc of four primogen have allied themselves in order to push through agendas. Anytime a long-term voting bloc enters the arean, elders outside the bloc are going to experience frustration. Little can be done about the bloc until it crumbles under internal pressure or the prince intercedes due to questionable agendas. If the bloc itself becomes too powerful, and the Prince attempts to intercede, the Prince herself may become a victim of the bloc, in worst case scenarios, a justicar may be sent to remove one or all members of the bloc.
Strong, Balanced Democratic Council Under a Strong Prince
This is an ideal state, if the parties involved can refrain from killing each other. In this state, neither the prince or the primogen can push through an agenda (or in the case of the Prince, act in an autocratic manner). This arrangement cannot work unless the prince is on relatively good terms with the primogen. Unfortunately, a butting of heads can occur if the prince and counsil are divided on an issue, hostility can erupt which may even result in the expulsion of the Prince. The benefactors of this type of counsel are really the camarilla of the city. With a strong prince and counsel who are able to deal with city affairs and city threats in a timely rational way, individuals in the city are safer and freer to go about their nightly activities.
Weak Council Under a Strong Prince
In this situation, the primogen are little more than advisors or a rubber stamp brigade. The prince introduces proposals, the council okays them, and that's that. If the prince is relatively ethical, such arrangements are necessarily bad, its certainly an efficient way to approach things.
Weak Council Under a Weak Prince
Among the worst arrangements in the Cammarilla is a situation where a weak prince oversees a weak primogen council. Under such conditions, order barely holds sway. Elysium in such cases is typically controlled by unofficial "warlords" (i.e. any Kindred with enough charisma or ray power to convince others to side with her instead of any of the othe elders) who can, if they so choose run roughshod over the traditions of the Camarilla. As order breaks down, so do the distinctions between Camarilla and Sabbat. Cities following this model are often refuges for the unaligned, if not for actual members of the Sabbat itself. This is the kind of city the archons are most likely to visit with notable frequency. it is not uncommoin for archons to be instructed to be looking for Kindred in the city who would make better primogen than those currently in office. The interesting thing about cities with such weak leadership is where the power does lie. Power is always somewhere, and if its hidden, there's generally a reason, cities with weak power structures may actually be largely in the hands of Giovanni, Setites, or other outside institutions.
The Advisory Council
In this case, the prince is the ultimate authority with regard to Kindred matters in the city. There is no democratice vote of the primogen council to determine anything, only the decree of the Prince after she has heard the opinions of the primogens.
Some Strange Cases
Democracy is not necessarily seen as an inherent good by all (or even most) elder Kindred. Too muich democracy can lead to a lowest-common-denominator rule that serves no one well. left to thir own devices, Kindred power structures can wax Byzantine. Ghent has three Ventrue primogen, two Toreador primogen, a Tremere whip with a vote on council matters, and a Tremere Prince who's vote counts twice. While they continue to have a Gangrel Primogen, they do not have an Assamite representative on the council, and probably won't until a new prince comes into office. In the city of Venice, on the other hand, had no Gangrel or Assamite primogen, but does have seven voices weighing in on policy issues - the seventh is provided by a family representative of Clan Giovanni.
In Fort Worth, Texas, which is just a half hour away from Dallas, the city lost its prince, and the primogen council has never seated a new regent. Instead, they are shadowed by the Prince of Dallas, who allows the council to exist to manage the affairs of the smaller city. The council reports their formal decisions to the Prince of Dallas who may veto or approve the decision. In this way, the Kindred of Fort Worth maintain some autonomy, and the Prince of Dallas maintains a much larger territory.