So I will probably never use a level 17 antipaladin, but out of curiosity, does aura of depravity stack with everything?
Each enemy within 10 feet takes a –4 penalty on saving throws against compulsion effects.
Specifically, does it stack with aura of cowardice and aura of despair?
causes all enemies within 10 feet to take a –4 penalty on saving throws against fear effects.
enemies within 10 feet of an antipaladin take a –2 penalty on all saving throws. This penalty does not stack with the penalty from aura of cowardice.
I assume these are all typless penalties and stack with each other unless they specifically say they don't (despair says it doesnt stack with cowardice). Is despair not stacking with cowardice a case of specific trumping general? Or is it a case of the authors using a stacking rule of which I am not aware. As I understand typeless penalty stacking, despair stacks with depravity (total -6), and would also stack with cowardice (total -8) for an effect that is both fear and compulsion (if that exists).
To answer my own question, I found this in the CRB.
Bonus Types: Usually, a bonus has a type that indicates how the spell grants the bonus. The important aspect of bonus types is that two bonuses of the same type don't generally stack. With the exception of dodge bonuses, most circumstance bonuses, and racial bonuses, only the better bonus of a given type works (see Combining Magical Effects). The same principle applies to penalties—a character taking two or more penalties of the same type applies only the worst one, although most penalties have no type and thus always stack. Bonuses without a type always stack, unless they are from the same source.
Penalties work the same way as bonuses. No special rules. Typeless penalties stack unless something indicates otherwise or unless the penalties are from the same source. This would mean that whether intended or not, aura of despair stacks with aura of depravity, and depravity would stack with cowardice if there was an effect that was both compulsion and fear (for example, maybe miasmal dread and signature skill: intimidate)
Is despair not stacking with cowardice a case of specific trumping general?
Yes; if it didn't explicitly say this, then the two abilities would stack since they are typeless penalties.
As I understand typeless penalty stacking, despair stacks with depravity (total -6), and would also stack with cowardice (total -8) for an effect that is both fear and compulsion (if that exists).
I don't believe there's any effect that's both a fear and compulsion effect, but that is how it would work. You could stack despair/depravity for -6 or cowardice/depravity for -8, so you would take the better bonus of the two in that case.
Fear effects are Necromancy and compulsions are Enchantment, so I don't think there are any normal spells/effects that are both. Words of Power allow a compound fear/compulsion wordspell, but that's the only way I remember off the top of my head.