How many seconds have you been in the room?
Let's say the time between t1 and t2 is 1 trillion seconds. Let us further assume that all people go through the rooms in the same amount of time (thus people spend 1 second each in room A, and 1 million seconds each in room B).
100 trillion of the 100.1 trillion observer moments between 0 and 1 seconds in a room occur in room A. All of the observer moments past 1 second occur in room B (this is somewhat flawed in that it is possible that the observers don't all spend the same amount of time in a given room, but even in the case where 100 million people stay in room A for 1 million seconds each, and the rest spend zero time, an observer who's been in a room for 1 million seconds is still overwhelmingly likely to be in room B. So basically the longer you've been in the room, the more probably you should consider it that you're in room B).
If an observer doesn't know how long they've been in a given room, I'm not sure how meaningful it is to call them "an" observer.
I have taken the survey.
What does 0.01% on the wrong answer get you?
It was a memetic hazard.
(not really)
I'm not sure, not having read the paper, but I would expect that "Lifetime manic features at age 22-23 years" means "number of manic features experienced in the time prior to 22-23 years of age" (i.e. we measured IQ of a bunch of 8-year-olds 15 years ago, and those people are now in the range of 22-23 years of age, and we ask how many manic episodes they've had in that time).
Why tunnels, not canals? Particularly in the case of Denver, you've got a huge elevation gain, so you'd need the locks anyway, and digging tunnels is expensive (and buying farmland to put your canal through is relatively cheap).
How difficult would this be, out of curiosity, keeping in mind that you don't need 100% accuracy? I can think of a couple approaches, though probably nothing that would be supported by any revenue model I can think of off the top of my head.
If those 100 billion true statements were all (or even mostly) useful and better calibrated than my own priors, then I'd be likely to believe you, so yes. On the other hand, if you replace $100,000 with $100,000,000,000, I don't think that would still hold.
I think you found an important caveat, which is that the fact that an agent will benefit from you believing a statement weakens the evidence that the statement is true, to the point that it's literally zero for an agent that you don't trust at all. And if an AI will have a human-like architecture, or even if not, I think that would still hold.
An interesting conclusion here is that if you save more than 2 minutes per mile (going 15 mph instead of 10mph, for example) of time sitting in traffic by riding a motorcycle instead of driving a car, the number of not-sitting-in-traffic minutes of your life actually increases by riding your bike.
Though note that the above calculation assumed that your risk of dying in a motorcycle crash while weaving through stopped traffic is not higher than 1/6 micromorts per mile. Also note that if your expected life span is 60 years, you now need to save 6 minutes per mile to "break even", which is unlikely -- if traffic is moving that slowly (remember that this is based on the average speed across the entire trip) you're probably better off walking.