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Probability quiz
Topic Started: May 28 2015, 02:03 PM (545 Views)
Horace
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HOLY CARP!!!
jon-nyc
May 30 2015, 01:11 AM
I'll say the halfer position is actually wrong because sleeping beauty does have new information. She knows she was awakened.
They'll tell you that she knew she would be awakened.

It's the awakening about whether she was awakened that matters.

It's a deep question?
As a good person, I implore you to do as I, a good person, do. Be good. Do NOT be bad. If you see bad, end bad. End it in yourself, and end it in others. By any means necessary, the good must conquer the bad. Good people know this. Do you know this? Are you good?
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jon-nyc
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Cheers
Waiting for Moonbat to offer his thoughts....
In my defense, I was left unsupervised.
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Moonbat
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Pisa-Carp
I also argued the answer was 1/3 but consider the following:

We seem to have established that we can alter the fairness of the coin wrt. Beauty by altering the number of wakening events associated with the coin falling heads/tails. In this case we only chose two wakening events for tails, but we could extend the experiment such that the number of wakening events is an arbitrary number and in doing so we can arbitrarily change the probability Beauty assigns the coin falling heads/tails. This also will work for a coin that is not fair to start with. Thus we can start with a biased coin that is 99% certain to fall heads and yet with a sufficient numbers of waking events associated with the coin falling tails we can create a situation such that Beauty would seem to be overwhelmingly confident that the coin is in fact tails.

That seems somewhat odd - if the coin is a million dollar lottery ticket (and by having numerous wakings associated with the ticket winning we've made her assign an overwhelmingly high likelyhood that the ticket has won) should Beauty immediately conclude she's won the lottery? If we provide her with a button which if pressed would claim the winning the lottery prize but at a cost (like paying $10,000) then it's easy to see that the expected utility of pressing such a button is negative if it's a one shot situation i.e. on multiple wakings pressing the button has no effect if she has already pressed the button. Yet that means beauty can wake up practically certain she's won the lottery yet equally certain she should not claim the winnings.
Entia non sunt multiplicanda praeter necessitatem
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jon-nyc
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Re your first paragraph: No we haven't affected coin toss probabilities. You need to consider we're not testing the proposition 'what are the odds that the coin is heads'. We're testing the proposition 'what are the odds that there is an awakening event at which the coin is heads?'

Re the second paragraph. ....


(deleted stuff that was insufficiently thought out. more later)
Edited by jon-nyc, Jun 1 2015, 06:30 AM.
In my defense, I was left unsupervised.
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Moonbat
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Pisa-Carp
Quote:
 
Re your first paragraph: No we haven't affected coin toss probabilities. You need to consider we're not testing the proposition 'what are the odds that the coin is heads'. We're testing the proposition 'what are the odds that there is an awakening event at which the coin is heads?'


During the experiment from the perspective of B aren't they the same?
Entia non sunt multiplicanda praeter necessitatem
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jon-nyc
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Presumably she's aware of the experiment design when deciding how she should answer. She kind of has to be. Otherwise you're just trolling her.


Experimenter: "So, Sleeping Beauty, we're going to flip a coin. What are the odds its heads?"

SB: "50%"

Experimenter: "Nope! Ha Ha! It's a trick coin, both sides are tails! You lose!"
In my defense, I was left unsupervised.
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Moonbat
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Well she's aware of the setup which is why she's assigning a probability of 1/3 to the coin being heads.

But it looks to me that from B's perspective 'what are the odds that the coin is heads' is equivalent to 'what are the odds that there is an awakening event at which the coin is heads'? which is why 1/3 is the right answer.

From the experimenter's perspective 'what are the odds that the coin is heads' gets a different answer but then the information they have is different.
Entia non sunt multiplicanda praeter necessitatem
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