This is my attempt at a pedagogical exposition of “the solution”. It’s overly long, and I've lost perspective completely about what is understood by the group here and what isn't. But since I've written up this solution for myself, I'll go ahead and share it.

The cases I'm describing below are altered from the OP so that they completely non-metaphysical, in the sense that you could implement them in real life with real people. Thus there is an objective reality regarding whether money is collectively lost or won, so there is finally no ambiguity about what the correct calculation actually is.

Suppose that there are twenty different graduate students {Amy, Betty, Cindy, ..., Tony} and two hotels connected by a breezeway. Hotel Green has 18 green rooms and 2 red rooms. Hotel Red has 18 red rooms and 2 green rooms. Every night for many years, students will be assigned a room in either Hotel Green or Hotel Red depending on a coin flip (heads --> Hotel Green for the night, tails --> Hotel Red for the night). Students won’t know what hotel they are in but can see their own room color only. If a student sees a green room, that student correctly deduces they are in Hotel Green with 90% probability.

Case 1: Suppose that every morning, Tony is allowed to bet that he is in a green room. If he bets ‘yes’ and is correct, he pockets $12. If he bets ‘yes’ and is wrong, he has to pay $52. (In other words, his payoff for a correct vote is $12, the payoff for a wrong vote is -$52.) What is the expected value of his betting if he always says ‘yes’ if he is in a green room?

For every 20 times that Tony says ‘yes’, he wins 18 times (wins $12x18) and he loses twice (loses $52x2), consistent with his posterior. One average he wins $5.60 per bet , or $2.80 per night. (He says “yes” to the bet 1 out of every 2 nights, because that is the frequency with which he finds himself in a green room.) This is a steady money pump in the student’s favor.

The correct calculation for Case 1 is:

average payoff per bet = (probability of being right)x(payoff if right)+ (probability of being wrong)x(payoff if wrong) = .9x18+.1x-52 =5.6.

Case 2: Suppose that Tony doesn’t pocket the money, but instead the money is placed in a tip jar in the breezeway. Tony’s betting contributes $2.80 per night on average to the tip jar.

Case 3: Suppose there is nothing special about Tony, and all the students get to make bets. They will all make bets when they wake in green rooms, and add $2.80 per night to the tip jar on average. Collectively, the students add $56 per night to the tip jar on average. (If you think about it a minute, you will see that they add $216 to the tip jar on nights that they are assigned to hotel Green and lose $104 on nights that they are assigned to hotel Red.) If the money is distributed back to the students, they each are making $2.80 per night, the same steady money pump in their favor that Tony took advantage of in Case 1.

Case 4: Now consider the case described in the OP. We already understand that the students will vote “yes” if they wake in a green room and that they expect to make money doing so. Now the rules are going to change, however, so that when all the green roomers unanimously vote “yes”, $12 are added to the tip jar if they are correct and $52 are subtracted if they are wrong. Since the students are assigned to Hotel Green half the time and to Hotel Red half the time, on average the tip jar loses $20 every night. Suddenly, the students are losing $1 a night!

Each time a student votes correctly, it is because they are all in Hotel Green, as per the initial set up of the problem in the OP. So all 18 green roomer votes are correct and collectively earn $12 for that night. The payoff is $12/18 per correct vote. Likewise, the payoff per wrong vote is -$52/2.

So the correct calculation for case 4 is as follows:

average payoff per bet = (probability of being right)x(payoff if right)+ (probability of being wrong)x(payoff if wrong) = .9x(18/12)+.1x(-52/2) = -2.

So in conclusion, in the OP problem, the green roomer must recognize that he is dealing with case #4 and not Case #1, in which the payoff is different (but not the posterior).

I don't understand how the examples given illustrate free-floating beliefs: they seem to have at least some predictive powers, and thus shape anticipation - (some comments by others below illustrate this better).

• The phlogiston theory had predictive power (e.g. what kind of "air" could be expected to support combustion, and that substances would grow lighter when they burned), and it was falsifyable (and was eventually falsified). It had advantages over the theories it replaced and was replaced by another theory which represented a better understanding. (I base this reading on Jim Loy's page on Phlogiston Theory.

• Literary genres don't have much predictive powers if you don't know anything about them - if you do, then they do. Classifying a writer as producing "science fiction" or "fantasy" creates anticipations that are statistically meaningful. For another comparison, saying some band plays "Death Metal" will shape our anticipation; somewhat differently for those who can distinguish Death Metal from Speed Metal as compared to those who merely know that "Metal" means "noise".

I can imagine beliefs leading to false anticipations, and they're obviously inferior to beliefs leading to more correct ones. That doesn't mean they're free-floating.

One example for the free-floating belief is actually about the tree falling in the forest: to believe that it makes a sound does not anticipate any sensory experience, since the tree falls explicitly where nobody is around to hear it, and whether there is sound or no sound will not change how the forest looks when we enter it later. However, to let go of the belief that the tree makes a sound does not seem to me to be very useful. What am I missing?

I understand that many beliefs are held not because they have predictive power, but because they generalize experiences (or thoughts) we have had into a condensed form: a sort of "packing algrithm" for the mind when we detect something common; and when we understand this commonality enough, we get to the point where we can make prediction, and if we don't yet, we can't, but may do so later. There is no belief or thought we can hold that we couldn't trace back to experiences; beliefs are not anticipatory, but formed from hindsight. They organize past experience. Can you predict which of these beliefs is not going to be helpful in organizing future experiences? How?

implicit lie vs. social fiction

I don't think these are normally useful ways of thinking about status posturing. Verbalising this stuff is a faux pas in the overwhelming majority of human social groups.

I'm not sure if I disagree with you on whether the message is "very likely" to be understood. In my limited experience, and with my below average people reading skills, I'd say that most status jockeying in non-intimate contexts is obvious enough for me to notice if I'm paying attention to the interaction.

The post you meant is probably Illusion of Transparency. I contend that it applies less strongly to in person status jockeying than to lingual information transfer. I suggest you watch a clip of a foreign language movie if you disagree.

Eliezer, you state in the intro that the 5-second-level is a "method of teaching rationality skills". I think it is something different.

First, the analysis phase is breaking down behaviour patterns into something conscious; this can apply to my own patterns as I figure out what I need to (or want to) teach, or to other people's patterns that I wish to emulate and instill into myself.

It breaks down "rationality" into small chunks of "behaviour" which can then be taught using some sort of conditioning - you're a bit unclear on how "teaching exercises" for this should be arrived at.

You suggest a form of self-teaching: The 5-second analysis identifies situations when I want some desired behaviour to trigger, and to pre-think my reaction to the point where it doesn't take me more than 5 seconds to use. In effect, I am installing a memory of thoughts that I wish to have in a future situation. (I could understand this as communcating with "future me" if I like science fiction. ;) Your method of limiting this to the "5-second-level" aims to make this pre-thinking specific enough so that it actually works. With practice, this response will trigger subconsciously, and I'll have modified my behaviour.

It would be nice if that would actually help to talk about rationality more clearly (but won't we be too specific and miss the big picture?), and it would be nice if that would help us arrive at a "rationality syllabus" and a way to teach it. I'm looking forward to reports of using this technique in an educational setting; what the experience of you and your students were in trying to implement this. Until your theory's tested in that kind of setting, it's no more than a theory, and I'm disinclined to believe your "you need to" from the first sentence in your article.

Is rationality just a behaviour, or is it more? Can we become (more) rational by changing our behaviour, and then have that changed behaviour change our mind?

My opinion? I'd not lie. You've noticed the attempt, why claim you didn't? Display your true reaction.

Noticing the attempt and doing nothing is not a lie. It is a true reaction.

Can you be more specific? What exactly are the dangers of neutralizing our "inner moralizers"?

Having brought up this topic, I find that I'm reluctant to now do the hard work of organizing my thoughts on the matter. It's obvious that the ability to moralize has a tactical value, so doing without it is a form of personal or social disarmament. However, I don't want to leave the answer at that Nietzschean or Machiavellian level, which easily leads to the view that morality is a fraud but a useful fraud, especially for deceptive amoralists. I also don't want to just say that the human utility function has a term which attaches significance to the actions, motives and character of other agents, in such a way that "moralizing" is sometimes the right thing to do; or that labeling someone as Bad is an efficient heuristic.

I have glimpsed two rather exotic reasons for retaining one's capacity for "judging people". The first is ontological. Moral judgments are judgments about persons and appeal to an ontology of persons. It's important and useful to be able to think at that level, especially for people whose natural inclination is to think in terms of computational modules and subpersonal entities. The second is that one might want to retain the capacity to moralize about oneself. This is an intriguing angle because the debate about morality tends to revolve around interactions between persons, whether morality is just a tool of the private will to power, etc. If the moral mode can be applied to one's relationship to reality in general (how you live given the facts and uncertainties of existence, let's say), and not just to one's relationship to other people, that gives it an extra significance.

The best answer to your question would think through all that, present it in an ordered and integrated fashion, and would also take account of all the valid reasons for not liking the moralizing function. It would also have to ground the meaning of various expressions that were introduced somewhat casually. But - not today.

I think you're misunderstanding what I said. I'm not obscuring my feelings from myself. I'm just aware of the moment when I choose what to feel, and I actively choose.

I'm not advocating never getting angry, just not doing it when it's likely to impair your ability to communicate or function. If you choose to be offended, that's a valid choice... but it should also be an active choice, not just the default.

I find it fairly easy to be frustrated without being angry at someone. It is, after all, my fault for assuming that someone is able to understand what I'm trying to argue, so there's no point in being angry at them for my assumption. They might have a particularly virulent meme that won't let them understand... should I get mad at them for a parasite? It seems pointless.

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If the message you intend to send is "I am secure in my status. The attacker's pathetic attempts at reducing my status are beneath my notice.", what should you do? You don't seem to think that ignoring the "attacks" is the correct course of action.

This is a genuine question. I do not know the answer and I would like to know what others think.

It could be. It seems not just difficult but actually against most culture on the planet. Consider that crimes of passion, like killing someone when you find them sleeping around on you, often get a lower sentence than a murder 'in cold blood'. If someone says 'he made me angry' we know exactly what that person means. Responding to a word with a bullet is a very common tactic, even in a joking situation; I've had things thrown at me for puns!

It does seem like a learn-able skill even so. I did not have this skill when I was child, but I do have it now. The point I learned it in my life seems to roughly correspond to when I was first trained and working as technical support. I don't know if there's a correlation there.

In any case, merely being aware that this is a skill may help a few people on this forum to learn it, and I can see only benefit in trying. It is possible to not control anger but instead never even feel it in the first place, without effort or willpower.

Edit - please disregard this post