In the two roleplays I am in currently (Pegasi and Centaurs, Shapeshifters) the process of how leaders gain power is central for the story.
For Pegasi and Centaurs, there are three main governments. The pegasi of Sun Herd have a single leader, Coalwing, who was earned his power through prowess in battle against other pegasi and became the top stallion in his herd. The village of Johirestown is governed by a council, with council members being elected due to merit or representing the military. The village of Irichad is governed by a chief, with a crown prince in line to inherit the familial rule.
For Shapeshifters, the isle of Animalia was originally ruled by the tyrannic Lion family. The Lion was overthrown and replaced by a 12 member council, each member representing an important family. Council seats are hereditary. Meanwhile, the Lion family leads a band of outcasts trying to regain power.
As you can see here, governance is widely varied and is sometimes debated across roleplays. What governments do your characters live under and do they support or contest them? If they had the ability, what government would they implement?