A player's allegiance rank is a function of the number of vassals and how they are organized. Specifically, take the two highest ranked vassals. The patron's rank will be one higher lower of the two or equal to the highest rank vassal, whichever is greater. For example, a patron with vassals of rank 5 and 7 would be rank 7. Rank 3 and 3 vassals would make the patron rank 4.
Loot items can have an allegiance rank requirement to activate the spells.
Below is the minimum number of followers for a given rank (many more will be required if not organized optimally).
There is a quest crown that raises rank by 1 for item activation purposes, but does not affect the player's rank title.