Obedience to the rule of your faction is measured in public order. The factors that affect it are displayed on the region details panel, and include elements such as settlement level, presence of a garrison and the size of the tax burden placed on the populace. If unhappiness begins to outweigh happiness it will accumulate, eventually leading to rebellion if left unchecked. Keep taxes at reasonable levels, maintain sufficient food supplies and ensure that settlements are garrisoned to stop low public order bubbling over into rioting or worse, full-scale rebellion.
The overall happiness of a population is influenced by a variety of different contributing factors, including tax levels, food shortages, the presence of entertainment and religious buildings, and repression through garrison size. Rebellion becomes a risk when the people are so unhappy that repression can no longer contain public order.
When unhappiness becomes too great the people will riot. The best ways to stop a riot, and prevent it from escalating into a rebellion, are to either reduce taxes to appease the rioters or increase the garrison, which in turn increases repression and crushes the riot. Factors which may cause a riot are: food shortages, taxation, the presence of rampaging enemy armies, and cultural unrest.