EPTcute example though ^.^
Bayesianism and Sleeping Beauty - Page 8
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sam!zdat
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cute example though ^.^ | ||
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Prog
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sam!zdat
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Reason
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Bayesianism 1 - 0 samzdat | ||
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sam!zdat
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If you think it's easy that means you don't understand yet, I promise edit: we can just generalize the above law to apply to all things, actually. That's the first dogma of the church of samizdat | ||
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Reason
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On January 05 2013 09:30 sam!zdat wrote: What's your solution? If you think it's easy that means you don't understand yet, I promise I think you're right, can you perhaps add a little bit about Bayesianism into the OP?? This requires prior knowledge which I don't have, and there's all sorts of stupid questions being asked and alternate problems and solutions throughout the thread. From what little I've read about Bayesianism and the question I *think* you're asking in the OP it all seems very simple to me, if you could perhaps clarify them both that would be helpful =) + Show Spoiler + not seeing the problem here If you want I can just read the OP as it is and give you my answer =/ Seems pointles if you're 100% certain I don't even understand the question lmao | ||
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sam!zdat
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yeah take a stab at it. what do you think | ||
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Reason
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She doesn't need to "gain" information about the world, she has already accumulated information throughout her life. She understands the inherent skullduggery in the philosopher's questioning and gives the appropriate answer... You need to specify if he must ask her this question when she wakes up or if he can opt not to ask if her the question, and she is aware of this too. If he promises that he will ask her the question any time that she wakes up then she will reply "The coin is less likely to have flipped tails than heads" if he doesn't say anything on the matter there's 3 options. 1. You make a random guess based on your previous life experience with mad philosophers 2. You try to determine what his aims are, work out how he will attempt to exploit your guessing pattern and play some kind of reverse double bluff on him. 3. Acknowledge that both are equally likely since he hasn't revealed if he will ask you the question every time or not, attribute a 50/50 chance that he does ask every time/doesn't ask every time which means overall heads is always the winning coin anyway, if you take this approach and I think it's the most "Bayesian" if my understanding is correct it will be something like 1/2 + 1/3 all divided by two. How did I do  ?edit: If you think it's easy that means you don't understand yet, I promise I smell a sig. | ||
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sam!zdat
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the problem is that on sunday it's obvious that the coin has .5 chance tails. when she wakes up (she doesn't know what day) she has gained no information (she can predict exactly what this waking up experience will be like) but all of the sudden it seems like the chance is 1/3 (that is, if you repeat and she always answers tails she will be wrong 2/3 of the time) | ||
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Sleeping Beauty: I say that proposition will be wrong 2/3 of the time/is most likely wrong sir. (my sleeping beauty is good at maths so would answer 50|50 before she slept after she woke up 1/3 | 2/3) | ||
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sam!zdat
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sam!zdat
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Try to imagine that you are in her situation. | ||
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I don't know enough about Bayesianism to give you a definitive answer. | ||
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sam!zdat
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The prior probability = 50/50 The two conditional probabilities are 1. one 2. infinity If the two conditional probabilities are equal, the posterior probability equals the prior probability. Since they're not she will give the answer of "I'm 99.999**% certain that I'm not going to be set free." I see why you've raised this issue, but I think it more highlights the counter-intuitive nature of statistics and probabilities to the human mind rather than shows that Bayesianism itself is flawed. | ||
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sam!zdat
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Reason
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Once she enters into the process of drinking potions, sleeping, waking up and drinking tea since she is going to be asked this question only once if she gets the good side of the coin and an infinite number of times if she gets the bad side of the coin the probability that this one particular day is the good day is 1 in infinity... Sorry, a better way of saying this would be: On any given day, because she doesn't know if it's the first day or nth day, from her perspective the chances are 50/50 that she will be let free, either she tossed heads or tossed tails. However, as people pointed out if you said tails every time you would be wrong 2/3 times for 1 day vs 2 day, so the actual probability of the question you're asking is very different to what a non-mathematician would intuitively answer. | ||
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sam!zdat
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