I agreed with your basic point in the haunted house article, while disagreeing with your theoretical analysis of it. Aumann was not wrong; obviously his conclusions follow from his premises. But it is also obvious that his premises do not apply perfectly to real people. Consequently, in the sense that people can be reasonable (which means not perfectly reasonable) and in which they can have reasonable beliefs (which means not perfectly reasonable beliefs) reasonable people can have reasonable beliefs which are in opposition to one another.
So I do not assume that someone else's belief is unreasonable as soon as he disagrees with me. I have at least one belief which would generally be considered to be a conspiracy theory. There is no reason for me to say what that belief is, because nearly all the readers of this comment would assume that I am wrong. And they would be perfectly reasonable in making that assumption, because judging from an outside view the belief would be very likely to be wrong. I do not think my belief is unreasonable, given my inside view, nor do I think the readers would unreasonable to assume that I am wrong, given their outside view.
Given someone that I consider overall reasonable, e.g. gjm, I am pretty sure that he and I could come to agreement regarding the truth of that belief, if we gave it sufficient time and discussion. But it almost certainly would not be worth the time and discussion, for either of us. Consequently there will necessarily be a persistent disagreement without that implying that anyone is unreasonable in the human sense of the term.
I think the same thing applies to religious / non-religious beliefs, at least in a general way, although I think that religious people have an extremely hard time distinguishing their motivations from their arguments (i.e. benefits from believing vs. evidence that those beliefs are true.) I know someone who seems to believe something like "My estimate based on my current evidence and analysis is that there is a 30% chance that my religion is true. Since there is a 70% chance it is false, it is probable that if I gave it sufficient thought and considered enough of the evidence, there is approximately a 70% chance that I could arrive at an estimate of a 99% chance it is false. But since I get instrumental benefits from believing, I do not intend to look at that evidence. So I will leave my estimate at 30%, which I am fairly comfortable with."
Personally I would never be comfortable with such a situation; I want to know what is actually true. But people care about different things, and I don't consider someone like that to be fundamentally unreasonable.
I grew up in an atheistic household.
Almost needless to say, I was relatively hostile towards religion for most of my early life. A few things changed that.
First, the apology of a pastor. A friend of mine was proselytizing at me, and apparently discussed it with his pastor; the pastor apologized to my parents, and explained to my friend he shouldn't be trying to convert people. My friend apologized to me after considering the matter. We stayed friends for a little while afterwards, although I left that school, and we lost contact.
I think that was around the time that I realized that religion is, in addition to being a belief system, a way of life, and not necessarily a bad one.
The next was actually South Park's Mormonism episode, which pointed out that a belief system could be desirable on the merits of the way of life it represented, even if the beliefs themselves are stupid. This tied into Douglas Adam's comment on Feng Shui, that "...if you disregard for a moment the explanation that's actually offered for it, it may be there is something interesting going on" - which is to say, the explanation for the belief is not necessarily the -reason- for the belief, and that stupid beliefs may actually have something useful to offer - which then requires us to ask whether the beliefs are, in fact, stupid.
Which is to say, beliefs may be epistemically irrational while being instrumentally rational.
The next peace I made with belief actually came from quantum physics, and reading about how there were several disparate and apparently contradictory mathematical systems, which all predicted the same thing. It later transpired that they could all be generalized into the same mathematical system, but I hadn't read that far before the isomorphic nature of truth occurred to me; you can have multiple contradictory interpretations of the same evidence that all predict the same thing.
Up to this point, however, I still regarded beliefs as irrational, at least on an epistemological basis.
The next peace came from experiences living in a house that would have convinced most people that ghosts are real, which I have previously written about here. I think there are probably good explanations for every individual experience even if I don't know them, but am still somewhat flummoxed by the fact that almost all the bizarre experiences of my life all revolve around the same physical location. I don't know if I would accept money to live in that house again, which I guess means that I wouldn't put money on the bet that there wasn't something fundamentally odd about the house itself - a quality of the house which I think the term "haunted" accurately conveys, even if its implications are incorrect.
If an AI in a first person shooter dies every time it walks into a green room, and experiences great disutility for death, how many times must it walk into a green room before it decides not to do that anymore? I'm reasonably confident on a rational level that there was nothing inherently unnatural about that house, nothing beyond explanation, but I still won't "walk into the green room."
That was the point at which I concluded that beliefs can be -rational-. Disregard for a moment the explanation that's actually offered for them, and just accept the notion that there may be something interesting going on underneath the surface.
If we were to hold scientific beliefs to the same standard we hold religious beliefs - holding the explanation responsible rather than the predictions - scientific beliefs really don't come off looking that good. The sun isn't the center of the universe; some have called this theory "less wrong" than an earth-centric model of the universe, but that's because the -predictions- are better; the explanation itself is still completely, 100% wrong.
Likewise, if we hold religious beliefs to the same standard we hold scientific beliefs - holding the predictions responsible rather than the explanations - religious beliefs might just come off better than we'd expect.