P(vulcan mountain | you're not in vulcan desert) = 1/3
P(vulcan mountain | guard says "you're not in vulcan desert") = P(guard says "you're not in vulcan desert" | vulcan mountain) * P(vulcan mountain) / P(guard says "you're not in vulcan desert") = ((1/3) * (1/4)) / ((3/4) * (1/3)) = 1/3
Woops, you're right; nevermind! There are algorithms that do give different results, such as justinpombrio mentions above.
EDIT: This was wrong.
The answer varies with the generating algorithm of the statement the guard makes.
In this example, he told you that you were not in one of the places you're not in (the Vulcan Desert). If he always does this, then the probability is 1/4; if you had been in the Vulcan Desert, he would have told you that you were not in one of the other three.
If he always tells you whether or not you're in the Vulcan Desert, then once you hear him say you're not your probability of being in the Vulcan Mountain is 1/3.
Definitely makes sense. A commonly cited example is women in an office workplace; what would be average assertiveness for a male is considered "bitchy", but they still suffer roughly the same "weak" penalties for non-assertiveness.
With the advice-giving aspect, some situations are likely coming from people not knowing what levers they're actually pulling. Adam tells David to move his "assertiveness" lever, but there's no affordance gap available for David by moving that lever -- he would actually have to move an "assertiveness + social skill W" lever which he doesn't have, but which feels like a single lever for Adam called "assertiveness". Not all situations are such; there's no "don't be a woman" or "don't be autistic lever". Sometimes there's some other solution by moving along a different dimension and sometimes there's not.
Feel similarly; since Facebook comments are a matter of public record, disputes and complaints on them are fully public and can have high social costs if unaddressed. I would not be worried about it in a small group chat among close friends.
I perceive several different ways something like this happens to me:
1. If I do something that strains my working memory, I'll have an experience of having a "cache miss". I'll reach for something, and it won't be there; I'll then attempt to pull it into memory again, but usually this is while trying to "juggle too many balls", and something else will often slip out. This feels like it requires effort/energy to keep going, and I have a desire to stop and relax and let my brain "fuzz over". Eventually I'll get a handle on an abstraction, verbal loop, or image that lets me hold it all at once.
2. If I am attempting to force something creative, I might feel like I'm paying close attention to "where the creative thing should pop up". This is often accompanied with frustration and anxiety, and I'll feel like my mind is otherwise more blank than normal as I keep an anxious eye out for the creative idea that should pop up. This is a "nothing is getting past the filter" problem; too much prune and not enough babble for the assigned task. (Not to say that always means you should babble more; maybe you shouldn't try this task, or shouldn't do it in the social context that's causing you to rightfully prune.)
3. Things can just feel generally aversive or boring. I can push through this by rehearsing convincing evidence that I should do the thing -- this can temporarily lighten the aversion.
All 3 of these can eventually lead to head pain/fogginess for me.
I think this "difficulty thinking" feeling is a mix of cognitive ability, subject domain, emotional orientation, and probably other stuff. Mechanically having less short-term memory makes #1 more salient whatever you're doing. Some people probably have more mechanical"spark" or creative intelligence in certain ways, affecting #2. Having less domain expertise makes #1 and maybe #2 more salient since you have less abstractions and raw material to work with. Lottery of interests, social climate, and any pre-made aversions like having a bad teacher for a subject will factor into #3. Sleep deprivation worsens #1 and #2, but improves #3 for me (since other distractions are less salient).
I think this phenomenon is INSANELY IMPORTANT; when you see people who are a factor of 10x or 100x more productive in an area, I think it's almost certainly because they've gotten past all of the necessary thresholds to not have any fog or mechanical impediment to thinking in that area. There is a large genetic component here, but to focus on things that might be changeable to improve these areas:
I really wish I had spent more time in the past working on these meta problems, instead of beating my head against a wall of brain fog.
A note on this, which I definitely don't mean to apply to the specific situations you discuss (since I don't know enough about them):
If you give people stronger incentives to lie to you, more people will lie to you. If you give people strong enough incentives, even people who value truth highly will start lying to you. Sometimes they will do this by lying to themselves first, because that's what is necessary for them to successfully navigate the incentive gradient. This can be changed by their self-awareness and force of will, but some who do that change will find themselves in the unfortunate position of being worse-off for it. I think a lot of people view the necessity of giving such lies as the fault of the person giving the bad incentive gradient; even if they value truth internally, they might lie externally and feel justified in doing so, because they view it as being forced upon them.
An example is a married couple, living together and nominally dedicated to each other for life, when one partner asks the other "Do I look fat in this?". If there is significant punishment for saying Yes, and not much ability to escape such punishment by breaking up or spending time apart, then it takes an exceedingly strong will to still say "Yes". And a person with a strong will who does so then suffers for it, perhaps continually for many years.
If you value truth in your relationships, you should not only focus on giving and receiving the truth in one-off situations; you should set up the incentive structures in your life, with the relationships you pick and how you respond to people, to optimally give and receive the truth. If you are constantly punishing people for telling you the truth (even if you don't feel like you're punishing them, even if your reactions feel like the only possible ones in the moment), then you should not be surprised when most people are not willing to tell you the truth. You should recognize that, if you're punishing people for telling you the truth (for instance, by giving lots of very uncomfortable outward displays of high stress), then there is an incentive for people who highly value speaking truth to stay away from you as much as possible.
I think you're looking for Thurston's "On proof and progress in mathematics": https://arxiv.org/abs/math/9404236
I think I may agree with the status version of the anti-hypocrisy flinch. It's the epistemic version I was really wanting to argue against.
Ok yeah, I think my concern was mostly with the status version-- or rather that there's a general sensor that might combine those things, and the parts of that related to status and social management are really important, so you shouldn't just turn the sensor off and run things manually.
... That doesn't seem like treating it as being about epistemics to me. Why is it epistemically relevant? I think it's more like a naive mix of epistemics and status. Status norms in the back of your head might make the hypocrisy salient and feel relevant. Epistemic discourse norms then naively suggest that you can resolve the contradiction by discussing it.
I was definitely unclear; my perception was the speaker's claiming "person X has negative attribute Y, (therefore I am more deserving of status than them)" and that, given a certain social frame, who is deserving of more status is an epistemic question. Whereas actually, the person isn't oriented toward really discussing who is more deserving of status within the frame, but rather is making a move to increase their status at the expense of the other person's.
I think my sense that "who is deserving of more status within a frame" is an epistemic question might be assigning more structure to status than is actually there for most people.
I will see if I can catch a fresh one in the wild and share it. I recognize your last paragraph as something I've experienced before, though, and I endorse the attempt to not let that grow into righteous indignation and annoyance without justification -- with that as the archetype, I think that's indeed a thing to try to improve.
Most examples that come to mind for me have to do with the person projecting identity, knowledge, or an aura of competence that I don't think is accurate. For instance holding someone else to a social standard that they don't meet, "I think person X has negative attribute Y" when the speaker has also recently displayed Y in my eyes. I think the anti-hypocrisy instinct I have is accurate in most of those cases: the conversation is not really about epistemics, it's about social status and alliances, and if I try to treat it as about epistemics (by for instance, naively pointing out the ways the other person has displayed Y) I may lose utility for no good reason.
As you say, there are certainly negative things that hypocrisy can be a signal of, but you recommend that we should just consider those things independently. I think trying to do this sounds really really hard. If we were perfect reasoners this wouldn't be a problem; the anti-hypocrisy norm should indeed just be the sum of those hidden signals. However, we're not; if you practice shutting down your automatic anti-hypocrisy norm, and replace it with a self-constructed non-automatic consideration of alternatives, then I think you'll do worse sometimes.
This has sort of a "valley of bad rationality" feel to me; I imagine trying to have legible, coherent thoughts about alternative considerations while ignoring my gut anti-hypocrisy instinct, and that reliably failing me in social situations where I should've just gone with my instinct.
I notice the argument I'm making applies generally to all "override social instinct" suggestions, and I think that you should sometimes try to override your social instincts -- but I do think that there's huge valleys of bad rationality near to this, so I'd take extreme care about it. My guess is I think you should override them much less than you do -- or I have a different sense of what "overriding" is.