Well, if the point of trolley problems is to gain some insight as to how we form moral judgments, I don't necessarily do even that particularly well. I suspect they don't even do that particularly well, since I suspect many respondents are going to give what they think is the approved answer, which is possibly different from what they would actually do. At best they provide insight as to why we might think of certain actions as moral or immoral.
But I sometimes see things like trolley problems used argue that there is something wrong with peoples' decision making processes, based on apparent inconsistencies in their responses. I think this is a crock. The fact is, we often have to make decisions very quickly based on woefully incomplete information. Yes we use heuristics, and yes sometimes which heuristic gets applied (and thus which choice we make) depends on how the problem is phrased, and that means sometimes we will give "inconsistent" answers. This is not a defect, it is the inevitable result of not having the luxury of infinite time to consider one's response.
At each step it's pretty easy to calculate the probability that the patient has each disease, and the probability that the patient will die if untreated.
You can get a .5 chance of saving the patient if you simply choose to treat for one disease and stick with that treatment. Let me arbitrarily say that if I choose this option I will treat for fungus.
I think a simple one move look ahead can give the optimum strategy: compare the chance of the patient dying on this turn to the chance of waiting saving the patient's life. It doesn't do any good to wait for more evidence if the extra evidence won't change your treatment anyway. So the chance of waiting saving patient is the confidence that you will have correctly identified the disease after waiting an extra turn minus .5 if changes your treatment and zero otherwise.
For example, if I have 1 red and one black card already and have not yet treated the patient and 4 turns have gone by, the chance of the patient dying next turn is I think 4/36. The the chance of waiting saving the patient's life is .5 .5 (x - .5) where the number x which I am too lazy to calculate is the probability the patient has an allergy given two black cards and one red one. (The first .5 is because there's only a coin flip chance of getting test results, the second because if I draw a red card it won't change my mind how to treat the patient).
Well, I don't think the analogy holds up all that well. In the coin flip story we "know" that there was a time before the universe with two equally likely rules for the universe. In the world as it is, AFAIK we really don't have a complete, internally consistent set of physical laws fully capable of explaining the universe as we experience it, let alone a complete set of all of them.
The idea that we live in some sort of low entropy bubble which spontaneously formed in a high entropy greater universe seems pretty implausible for the reasons you describe. But I don't think we can come to a conclusion from this significantly stronger than "there's a lot we haven't figured out yet".
I don't see any problem with acknowledging that in a world very different from this one my beliefs and actions would also be different. For example, I think the fact that there are and have been so many different religions with significantly different beliefs as to what God wants is evidence that none of them are correct. It follows that if there was just one religion with any significant number of adherents then that would be evidence (not proof) that that religion was in fact correct.
Maybe if Omega tells me it's Catholicism or nothing I'll become a Catholic. Maybe if he says it's the Aztec religion or nothing I'll cut out your beating heart and toss you down a pyramid. But no worries, neither one is going to happen in the real world.
The confusion is because you are trying to do two contradictory things with your "vote". If the goal is to inform future readers as to whether a post is high quality or low quality, clearly you should just give your personal assessment. The only reason you'd take priors into account was if your "vote" was actually a "bet" and there was some advantage to "betting" correctly.
I'd rephrase this to emphasize the nonboolean nature of belief: an aspiring rationalist should seek to make his degree of belief in a proposition correspond to the strength of the evidence. It is also an error to have excessive confidence in a proposition that is most likely true.
I'm not sure I've "learned" anything. You've largely convinced me that we don't really "know" anything but rather have varying degrees of belief, but I believed that to some degree before reading this site and am not 100% convinced of it now.
The most important thing I can think of that I would have said is almost certainly wrong before and that I'd say is probably right now is that it is legitimate to multiply the utility of a possible outcome by its probability to get the utility of the possibility.
I haven't yet seem anyone assert that the First Amendment should only apply to journalists. I occasionally see implications that members of accredited news organizations should enjoy immunity from prosecution for espionage, libel, etc. but that's not quite the same thing. If you mean to imply that the existence of espionage laws is a clear violation of the First Amendment, you probably should state it explicitly, since that is not a commonly help proposition.
Or was this a deliberate illustration of the phenomenon the post was describing?