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PaperclipPerfector  5d ago (text post)   19983 thread views

Culture War Roundup for the week of November 10, 2025

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Okay, but what if Bob is a Christian baby…?

Maybe it’s the fact that it’s the end of a long day, or because I dealt with an AI-psychotic crackpot earlier, but I can’t follow this at all. Surely there’s a more elegant framing.

I definitely don’t see why it’s culture war. Not unless this is a devious way to criticize the woke left.

The culture war angle is that the correct answer is 1/3 and that the people who think it is 1/2 cannot comprehend a word problem and need to be put into UCSD's remedial mathematics course.

Can't tell if really good joke because that's what we actually see the culture warriors roll with... or if actually missed the point.

I phrased it a bit flippantly, but I do think that the original question is not ambiguously phrased. We do not say that people who think that there is no advantage to switching doors in the Monty Hall problem are answering a different question than the people who say that there is an advantage to switching. We say they are wrong.

We do not say that people who think that there is no advantage to switching doors in the Monty Hall problem are answering a different question than the people who say that there is an advantage to switching. We say they are wrong.

It depends on how it's phrased. If they are given the proper version of the Monty Hall problem, then 1/2 is wrong. But if the problem description is sloppy and underspecified then it's legitimately ambiguous and they ARE answering a different question (The Monty Fall problem) correctly. Half the confusion with the Monty Hall problem is that midwits who are trying to be clever but don't fully understand the logic give an underspecified version of the problem half the time and don't notice, or do it deliberately to invite ambiguity so they get opportunities to smugly correct people.

Verily, in the Monty Hall problem. There, you actually do have a very very clear moment where information is gained and there is no ambiguity about which question you are being asked. But in this problem, if Alice tells Bob what you seem to want to have her tell him, we would say that she is wrong. We'd even say that she's extra wrong if she said she "updated".

Sorry, my comment was ambiguously phrased. I was referring to the cannonical form of the Sleeping Beauty question from Wikipedia:

Sleeping Beauty volunteers to undergo the following experiment and is told all of the following details: On Sunday she will be put to sleep. Once or twice, during the experiment, Sleeping Beauty will be awakened, interviewed, and put back to sleep with an amnesia-inducing drug that makes her forget that awakening. A fair coin will be tossed to determine which experimental procedure to undertake:

  • If the coin comes up heads, Sleeping Beauty will be awakened and interviewed on Monday only.
  • If the coin comes up tails, she will be awakened and interviewed on Monday and Tuesday.
  • In either case, she will be awakened on Wednesday without interview and the experiment ends.

Any time Sleeping Beauty is awakened and interviewed she will not be able to tell which day it is or whether she has been awakened before. During the interview Sleeping Beauty is asked: "What is your credence now for the proposition that the coin landed heads?"

This question is not ambiguous. The correct answer is 1/3. If you ran this experiment on people who think the answer is 1/2 you could take their money.

Are you taking Alice's money or Bob's money? From what I can see, they've got a nice system set up that's not letting you take their money, but it's not the case that the only number involved in their system is 1/3.

I think there's a sort of Monty Hall-style switcharoo going on with regards to what Alice puts into the computer. Only what she puts in the computer on Monday matters, so she should put the probability conditional on it being Monday into the computer, but bet her true probability (since she doesn't know whether or not it is Monday) herself.

So, I wanted to give you an opportunity to suggest your own name and conceptual meaning for the number that Alice puts into the computer in Variant 2 before I gave my own take on it. I think at this point, you've had an opportunity and have not taken it, so here goes.

I cannot think of anything that is appropriate to call this number (the number that Alice puts into the computer in Variant 2) other than some form of "the probability that Bob observes an outcome". Alice has to be reasoning about Bob's observation function when she computes this number. It's pretty obvious, because if we keep everything else the same, but fiddle with Bob's observation function, then we see a corresponding change in Alice's computation and the resulting value of this number (and no other change in Alice's reasoning or behavior, as evidenced by her own bets).

As such, if I can put it in a pointed way, why would one think that Alice is smart enough and capable of distinguishing between "the probability that Bob observes an outcome" and "the probability of the coin flip, itself"... but is too stupid to distinguish between "the probability that I, Alice, observe an outcome" and "the probability of the coin flip, itself"?

You're being shifty with your language, though. First, you have an underspecified "probability conditional on it being Monday". I'm being a bit picky with this one, but please fully state "probability of ______" even if you think it's "...conditional on it being Monday". Second, you have that she is supposed to bet her "true probability", but what do you mean by "true" probability? This phrase is not defined. "True probability" of what?

Notice further that there are three variants. She doesn't always put the same number in the computer in each variant. How does that work? What name would you call the number that Alice puts into the computer in Variant 2, for example?

I think it's more or less coherent, but the more elegant framing is already established by the Groisman paper. It is a bit excessively long for what's its trying to say though. The TLDR is:

There are two different probability spaces being discussed in the canonical problem. People implicitly switch between them mid-argument. Once you keep them separate, there is no paradox.

I'm pretty sure @ControlsFreak is just making the two probability spaces explicit by assigning them to Alice and Bob, rather than both to Beauty.

edit: I guess the culture war angle is twofold. One is epistemic, what does it mean to know or have information. Two, Grokipedia said the solutions to the problem are controversial. This was disputed as incorrect since the truth is obvious, but the subsequent dispute proves by example it is in fact controversial. Thus showing Grokipedia in fact spewing hard truths the woke left don't want you to know (mostly /s).

I definitely agree that Groisman did it. I think that Groisman's very slight issue with the pre-filling of the box has apparently left a lot of people unconvinced. They're still publishing papers about it!

So, what I think is useful about my framing is that 1) It doesn't have this issue. Everything is very cleanly just in line with the original Sleeping Beauty setup. Alice is still even making her same bets! 2) I think more important than assigning them to Alice and Bob, my setup with the computer communication is demonstrating that Alice is, herself, retaining knowledge of the different probability spaces. You know this, because you can get her to tell you this (through the computer and her own bets). Even if you just had Alice and Bob doing independent experiments, one could very plausibly still go off the deep end of weird anthropics. By forcing all the conceptual distinctions to be contained within one hypothetical brain, I think you're pretty forced to realize that one brain can, indeed, hold different probabilities for different purposes, rather than "updating" your worldview because they sound similar at first glance or whatever weird timeline causality argument you want to twist your brain into.

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