I'll start with a confession:
The evidence I have personally seen suggests haunted houses are, in fact, real, without given any particular credence to any particular explanation of what the haunting is. In particular, I own a house in which bizarre crap has happened since I first moved into it. Persistently. I've moved into another house, and have been making repairs in preparation to sell it; most recently, in a room with almost no furniture, in a space with absolutely no furniture, a key was dropped by myself. Four people searched the area for significant periods of time on three different occasions with no luck. I found it on the floor a week or two ago on top of something that wasn't there when it fell. Which is the straw that broke the camel's back in terms of my skepticism.
Other bizarre things that have happened include such things as my waking up to discover my recently-purchased bottle of key lime juice had been placed in the oven, and the oven turned on; the plastic bottle had just started to melt when I made the discovery. Another situation involved my sister, who one morning (while home alone) walked into the living room and discovered on a previously empty floor three sonograms of the previous occupant's baby. (There were -many- other things; I'm choosing for the purposes of this post the most unusual and least prone-to-outside-explanation occurrences. Night terrors, for example, are easily explained.)
Up until the last incident, the key, I was inclined to attribute the events to, say, sleepwalking and confirmation bias. At this point, I do not think the evidence really supports that conclusion anymore. My skepticism has been broken by personal experience; I'm not going to attribute anything to any -particular- explanation, but there is definitely something -not normal- about that house, whatever it may be; it has been the (nearly) sole repository of such experiences in my life. (The only other such experience was the day my grandfather (with whom I was extremely close) died, and given the mental turmoil I was experiencing, I'm disinclined to give that particular experience too much credit. For the curious, I was taking a shower, and the hot water repeatedly (3 times) turned off. As in, the knob was completely rotated to shut off the flow of hot water to the faucet.)
A key point of rationality is that evidence can in fact change your mind. Well, the evidence has changed my mind.
From a reader's perspective, this is all anecdotal evidence. So I don't expect to change anybody -else's- mind - indeed, you're probably making a mistake if you -do- change your mind, because out of millions of people, you -should- expect to see a few weird things being related by other people. The odds of somebody else relating an entirely factual series of anecdotes that suggest something unlikely are probably significantly higher than the odds of that unlikely thing being true. However, the odds of such things happening to you personally are considerably -lower- than the odds of hearing about the events from somebody else. Which all leads into a central conclusion: It's possible for the evidence to support one person believing something, while at the same time -not- supporting that anybody else believe that thing. If you win the lottery, that may be evidence for you believing you're living in a simulation or that some other mechanism "forced" the outcome - while at the same time the evidence doesn't suggest anything for somebody -else- winning the lottery.
I have a different purpose in mind: Making the claim that objectively irrational beliefs can, in fact, be subjectively rational. Prior to these experiences, I regarded the idea of a haunted house - I use the idea without prejudice for what "haunted" is or refers to - was that it was just superstitious people scaring themselves. At this point I'm forced by the evidence I've seen to conclude that there's something to the idea, even if it's not what people think it is. Maybe EMFs subtly messing with my brain (there is some weak evidence for the idea that electromagnetic fluctuations can induce metabolic changes in neurons - see http://jama.jamanetwork.com/article.aspx?articleid=645813 ), maybe something else.
If a pattern-recognition algorithm doesn't produce false positives, it's probably getting false negatives, and given that we can test false positives but do not know to test false negatives, pattern-recognition should favor false positives over false negatives. What does this have to do with anything? Well, it means superstitions aren't a product of a poor mind, only -untested- superstitions are. A good intelligence should develop superstitions. It should, when capable, discard them.
But it should only discard such superstitions as it has evidence to do so.
Now, the skeptical reader might ask what odds I place on each of these events occurring. My answer is as follows: Each event was highly unlikely in itself, explainable as an independent event only by positing pretty unlikely circumstances (what odds would I place on me or my housemate sleepwalking multiple times when neither of us have any history of such behavior, and such behavior has entirely ceased since leaving that house? Keep in mind that neither I nor my sister were initially inclined to regard such events as even needing explanation; it's only been until the most recent episode that I've decided the evidence suggests anything at all, so the possible explanation that the sleepwalking was a product of disturbance at the first few unusual events seems unlikely). Further evidence has rendered each event less likely as an independent phenomenon - since moving to a different house, the occurrences have ceased. When returning to the house, occurrences resume within its context. My control, while hardly blind, is controlling. But meaningfully, the same evidence doesn't mean the same thing if it is coming from somebody else; out of millions of people, I would expect such things to occur. I simply cannot expect them to occur -to me-. (And I wasn't the only one who found the house to be... off. There's a sense of not-quite-rightness to one basement room which I cannot explain without resorting to Lovecraftian cliches about alien geometries. The house was burgled several times; the only room that was left completely untouched, even when the copper piping was stolen (and subsequently the water meter - I got a waterfall in my basement!), was that room, which is conveniently where I left a thousand or so dollars worth of building materials for a project I hadn't finished yet.)
Evidence is personal. The odds of something happening are not equal to the odds of that something happening to you. Therefore, while we should not be surprised if miracles (that is, really unlikely and contextually significant events) occur, it is still legitimate to be surprised when they occur to us individually. The qualitative rationality of an individual belief is not equal to the qualitative rationality of the same belief on a social scale; individuals get different evidence than society, even when the same evidence is apparently present both for the individual and the community.
And just as it is a mistake for people to judge the beliefs of others based on the community standard of evidence, rather than the individual standard of evidence, it is likewise a mistake for an individual to judge society based on the individual standard of evidence, rather than the community. Just as it is possible for the individual to rationally believe something that society should not rationally believe as a whole, it is possible for society to rationally reject something the individual has overwhelming personal evidence for.
Aumann was, in short, wrong, because Aumann Updating is based on the belief that two individuals -can- share evidence. Evidence is incompletely transferable.
(Note: Anthropic reasoning can potentially remedy this at least to some extent for -past- experiences; reproducible and continuing experiences somewhat less.)