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All of Duschkopf's Comments + Replies

Beauty and the Bets
Duschkopf10

„And why did you happen to decide that it's P(Tails|Tails) = 1 and P(Heads|Tails) = 0 instead of P(Heads|Heads) = 1 and P(Tails|Heads) = 0 which are "relevant" for you decision making?  You seem to just decide the "relevance" of probabilities post hoc, after you've already calculated the correct answer the proper way. I don't think you can formalize this line of thinking, so that you had a way to systematically correctly solve decision theory problems, which you do not yet know the answer to. Otherwise, we wouldn't need utilities as a concept.“

No, it‘... (read more)

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Semantic Disagreement of Sleeping Beauty Problem
Duschkopf*20

If this were true that the concept of „indexical sample space“ does not capture the thirder position, how do you explain that it produces exactly the same probabilities that thirders entertain? Operating with indexicals is a necessary condition (and motivation) for Thirdism, which means assuming indexical sample spaces when it comes to the mathematical formalization of arguments in terms of probability theory. To my knowledge no relevant thirder literature denies that. And within the thirder model, these probabilities indeed hold true. If we assume Monday ... (read more)

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Beauty and the Bets
Duschkopf30

„Whether or not your probability model leads to optimal descision making is the test allowing to falsify it.“

Sure, I don‘t deny that. What I am saying is, that your probability model don‘t tell you which probability you have to base on a certain decision. If you can derive a probability from your model and provide a good reason to consider this probability relevant to your decision, your model is not falsified as long you arrive at the right decision. Suppose a simple experiment where the experimenter flips a fair coin and you have to guess if Tails or Hea... (read more)

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1Ape in the coat
It says which probability you have, based on what you've observed. If you observed that it's Monday - you are supposed to use probability conditionally on the fact that it's Monday, if you didn't observe that it's Monday you can't lawfully use the probability conditionally on the fact that it's Monday. Simple as that. There is a possible confusion where people may think that they have observed "this specific thing happened" while actually they observed "any thing from some group of things happened", which is the technicolor and rare event cases are about. Here you are confusing probability and utility. The fact that P(Heads)=P(Tails)=1/2 is very much relevant to our decision making! The correct reasoning goes like this: P(Heads) = 1/2 P(Tails) = 1/2 U(Heads) = 0 U(Tails) = X, E(Tails) = P(Tails)U(Tails) - P(Heads)U(Heads) = 1/2X - 0 Solving E(Tails) = 0 for X: X = 0 Which means that you shouldn't bet on Heads at any odds And why did you happen to decide that it's P(Tails|Tails) = 1 and P(Heads|Tails) = 0 instead of P(Heads|Heads) = 1 and P(Tails|Heads) = 0 which are "relevant" for you decision making?  You seem to just decide the "relevance" of probabilities post hoc, after you've already calculated the correct answer the proper way. I don't think you can formalize this line of thinking, so that you had a way to systematically correctly solve decision theory problems, which you do not yet know the answer to. Otherwise, we wouldn't need utilities as a concept.  This is not "another way". This is the right way. It has the proper formalization and actually allows us to arrive to the correct answer even if we do not yet know it. You do not "ignore your total evidence" - you are never supposed to do that. It's just that you didn't actually receive the evidence in the first place. You can observe the fact that the room is blue in the experiment only if you put your mind in a state where you distinguish blue in particular. Until then your event space doesn't
Beauty and the Bets
Duschkopf30

Honestly, I do not see any unlawful reasoning going on here. First of all, it‘s certainly important to distinguish between a probability model and a strategy. The job of a probability model is simply to suggest the probability of certain events and to describe how probabilities are affected by the realization of other events. A strategy on the other hand is to guide decision making to arrive at certain predefined goals.

My point is, that the probabilities a model suggests you to have based on the currently available evidence do NOT neccessarily have to matc... (read more)

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1Ape in the coat
Of course. As soon as we are talking about goals and strategies we are not talking about just probabilities anymore. We are also talking about utilities and expected utilities. However, probabilities do not suddenly change because of it. Probabilistic model is the same, there are simply additional considerations as well.  Whether or not your probability model leads to optimal descision making is the test allowing to falsify it. There are no separate "theoretical probabilities" and "decision making probabilities". Only the ones that guide your behaviour can be correct. What's the point of a theory that is not applicable to practice, anyway? If your model claims that the probability based on your evidence is 1/3 but the optimal decision making happens when you act as if it's 1/2, then your model is wrong and you switch to a model that claims that the probability is 1/2. That's the whole reason why betting arguments are popular. Questions of what "counts" or "matters" are not the realm of probability. However, the Beauty is free to adjust her utilities based on the specifics of the betting scheme. The model says that  P(Heads|Red) = 1/3  P(Heads|Blue) = 1/3 but P(Heads|Red or Blue) = 1/2 Which obviosly translates in a betting scheme: someone who bets on Tails only when the room is Red wins 2/3 of times and someone who bets on Tails only when the room is Blue wins 2/3 of times, while someone who always bet on Tails wins only 1/2 of time. This leads to a conclusion that observing event "Red" instead of "Red or Blue" is possible only for someone who has been expecting to observe event "Red" in particular. Likewise, observing HTHHTTHT is possible for a person who was expecting this particular sequence of coin tosses, instead of any combination with length 8.  See Another Non-Anthropic Paradox: The Unsurprising Rareness of Rare Events
Beauty and the Bets
Duschkopf10

Sure, if the bet is offered only once per experiment, Beauty receives new evidence (from a thirder‘s perspective) and she could update.

In case the bet is offered on every awakening: do you mean if she gives conflicting answers on Monday and Tuesday that the bet nevertheless is regarded as accepted?

My initial idea was, that if for example only her Monday answer counts and Beauty knows that, she could reason that when her answer counts it is Monday, arriving at the conclusion that it is reasonable to act as if it was Monday on every awakening, thus grounding her answer on P(H/Monday)=1/2. Same logic holds for rule „last awakening counts“ and „random awakening counts“.

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1Ape in the coat
Yes I do.  Of course, if the experiment is run as stated she wouldn't be able to give conflicting answers, so the point is moot. But having a strict algorithm for resolving such theoretical cases is a good thing anyway. Yes, I got it. As a matter of fact this is unlawful. Probability estimate is about the evidence you receive not about what "counts" for a betting scheme. If the Beauty receives the same evidence when her awakening counts and when it doesn't count she can't update her probability estimate. If in order to arrive to the correct answer she needs to behave as if every day is Monday it means that there is something wrong with her model. Thankfully for thirdism, she does not have to do it. She can just assign zero utility to Tuesday awakening and get the correct betting odds. Anyway, all this is quite tangental to the question of utility instability. Which is about the Beauty making a bet on Sunday and then reflecting on it during the experiment, even if no bets are proposed. According to thirdism probability of the coin being Heads changes on awakening, so, in order for Beauty not to regret about making an optimal bet on Sunday, her utility has to change as well. Therefore utility instability.
Beauty and the Bets
Duschkopf10

Rules for per experiment betting seem to be imprecise. What exactly does it mean that Beauty can bet only once per experiment? Does it mean that she is offered the bet only once in case of Tails? If so, is she offered the bet on Monday or Tuesday or is the day randomly selected? Or does it mean that she is offered the bet on both Monday and Tuesday and only one bet counts if she accepts both? If so, which one? Monday bet, Tuesday bet, or is it randomly selected?

Depending on, a Thirder could base his decision on:

P(H/Today is Monday)=1/2, P(H/Today is my last awakening)=1/2, or P(H/Today is the randomly selected day my bet counts/is offered to me)=1/2

and therefore escapes utility instability?

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1Ape in the coat
There are indeed ways to obfuscate the utility instability under thirdism by different betting schemes where it's less obvious, as the probability relevant to betting isn't P(Heads|Awake) = 1/3 but one of thoses you meantion which equal 1/2. The way to define the scheme specifically for P(Heads|Awake), is this: you get asked to bet on every awakening. One agreement is sufficient, and only one agreement counts. No random selecting takes place. This way the Beauty doesn't get any extra evidence when she is asked to bet, therefore she can't update her credence for the coin being Heads based on the sole fact of being asked to bet, the way you propose.
Another Non-Anthropic Paradox: The Unsurprising Rareness of Rare Events
Duschkopf10

Maybe I expressed myself somewhat misleadingly. I am not saying that she is surprised because the coincidence is more unlikely than the sequence. You are absolutely right in correcting me that the latter isn‘t even the case (also since P(HHTHTHHT/„HHTHTHHT“)=P(HHTHTHHT)=1/2^8). What I was trying to say is that her suprise about the coincidence arises from the circumtance that the coincidence is both unlikely and looks like a pattern. That fact that an event is unlikely is a necessary condition to be surprised about its occurence but not a sufficient condit... (read more)

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1Ape in the coat
When you are tracking event A you are automatically tracking its complement.  Oh sure, you are of course completely correct here. But this doesn't contradict what I'm saying.  The thing is, we observe a particular outcome and then we see which event(s) it corresponds to. Let's take an example: a series of 3 coin tosses.  So, in the beginning you have sample space which consist of all the elementary outcomes: {HHH,TTT,HHT,TTH,HTH,THT,THH,HTT} And an event space, some sigma-algebra of the sample space, which depends on your precommitments. Normally, it would look something like this: {∅,{HHH,TTT},{HHT,TTH,HTH,THT,THH,HTT},{HHH,TTT,HHT,TTH,HTH,THT,THH,HTT}} Because you are intuitively paying attention to whether there all Heads/Tails in a row. So your event space groups individual outcomes in this particular way, separating the event you are tracking and it's complement. When a particular combination, say THH is realized in a iteration of the experiment, your mind works like this: * Outcome THH is realized * Therefore every event from the event space which includes THH is realized. * Events {HHT,TTH,HTH,THT,THH,HTT} and {HHH,TTT,HHT,TTH,HTH,THT,THH,HTT} are realized. * P(HHT or TTH or HTH or THT or THH or HTT)=2/3 * This isn't a rare event and so you are not particularly surprised So, as you see, you do indeed observe an actual sequence, it's just that observing this sequence isn't necessary an event in itself.
Another Non-Anthropic Paradox: The Unsurprising Rareness of Rare Events
Duschkopf10

Yes. Our human mind is obviously biased to detect patterns. And people tend to react surprised if they observe patterns where they did not expect them to find. If someone has a specific sequence of coin toss results in her mind (eg. „HHTHTHHT“) and she is able to reproduce it with an actual coin on her first try, then she will likely be surprised. What she is really surprised about however, is not that she has observed an unlikely event ({HHTHTHHT}), but that she has observed an unexpected pattern. In this case, the coincidence of the sequence she had in m... (read more)

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1Ape in the coat
Why do you oppose these two things to each other? Talking about patterns is just another way to describe the same fact. Well, yes. Or you can say that having a specific combination in mind allowed to observe event "this specific combination" instead of "any combination". Once again this is just using different language to talk about the same thing. Oh! Are you saying that she has observed the intersection of two rare events: "HHTHTHHT was produced by coin tossing" and "HHTHTHHT was the sequence that I came up with in my mind" both of which have probability 1/2^8 so now she is surprised as if she observed an event with (1/2^8)^2? That's not actually the case.  If the person came up with some other combination and then it was realized on the coin tosses the surprise would be the same - there are 1/2^8 degrees of dreedom here - for every possible combination of Heads and Tails with lenghth 8. So the probability of the observed event is still 1/2^8.