I didn’t say it’s how you determine which is which in practice, I said (or meant to) it’s what I think each means. (Admittedly this isn’t the answer to Jayson’s question, but I wasn’t answering to that. I didn’t mean to say that everything that affects decisions is a preference, I just realized it might be interpreted that way, but obviously not everything that affects how you interpret evidence is a bias, either.)

I’m not sure I understand what you mean about aliefs. I thought the point of aliefs is that they’re not beliefs. E.g., if I alieve that I’m in danger because there’s a scary monster on TV, then my beliefs are still accurate (I know that I’m not in danger), and if my pulse raises or I scream or something, that’s neither bias nor preference, it’s involuntary.

The tricky part is if I want (preference) to go to sleep later, but I don’t because I’m too scared to turn off the light, even though I know there aren’t monsters in the closet. I’m not sure what that’s called, but I’m not sure I’d call it a bias (unless maybe I don’t notice I’m scared and it influences my beliefs) nor a preference (unless maybe I decide not to go to sleep right now because I’d rather not have bad dreams). But it doesn’t have to be a dichotomy, so I have no problem assigning this case to a third (unnamed) category.

Do you have an example of alief involvement that’s more ambiguous? I’m not sure if you mean "arbitrary" in practice or in theory or both.