Raising the authority of your king?

[FactionHeir]

Using a diplomat every turn (for a successful negotiation, not gifting), fighting, using assassins/spies, staying in towns with racing tracks/tourneys, using up all movement points, releasing or executing prisoners (not randoming), exterminating cities.

[Slaists]

Using assassins/spies works the best for me.

[Flavius Gonzo]

What does Authority affect? I haven't quite figured out yet why this is important.

Does it affect whether an unlead re-inforcement stack has a chance of turning rebel? If not, what does affect this? It's definitely annoying.

[FactionHeir]

It kind of acts as a boost for the loyalty of all your troops.
For captains the chance of turning rebel and for generals/family members the chance of getting bribed away.

Possibly some effect on diplomacy too, but not sure on that one

[katank]

The loyalty is the biggest thing. It really stinks to have your high valor captain led troops turn on you or a full stack of reinforcements to not make it.