That intuition pump doesn’t really work for me. The extreme cases seems to make it more apparent that thirding is correct.
There are ethical implications to accepting different assumptions about observation selection effects. For example, SSA has the possible assumption of a near term doomsday. One implication of the SIA, in my view, is that multiple existences is possible.
I'm still slightly confused here myself. My initial thoughts were quite strongly in the 1/2 camp, but Arjun makes a compelling case.
Something that confuses me still more- what probability should Beauty ascribe, on waking, to the day being Tuesday? Is it 1/2, 1/3 or 1/4? 1/2 seems clearly wrong to me, but the original proposer of 1/3 seemed to think it correct.
* All experiments feature a Monday awakening. Half of experiments feature a Tuesday one. So Tuesday awakenings are exactly half as common as Monday ones. So the probability must be 1/3.
* There's a 50% chance of Heads, in which case it is Monday for sure. There's a 50% chance of Tails, in which case there's a 50% chance it's Tuesday. So the probability is 1/4.
If you ask me before the experiment, 'What is the probability of the coin landing heads conditional on you waking up as a sleeping beauty test subject,' 1/3. So I would not update throughout the experiment and still be a 'thirder'. If you just asked for the probability of the coin landing heads, I would say 1/2, and then me waking up and being interviewed would be evidence of the type 'I am a sleeping beauty test subject' and would cause me to update to 1/3.
That intuition pump doesn’t really work for me. The extreme cases seems to make it more apparent that thirding is correct.
There are ethical implications to accepting different assumptions about observation selection effects. For example, SSA has the possible assumption of a near term doomsday. One implication of the SIA, in my view, is that multiple existences is possible.
If you wake up and I offer you a bet on what day it is, what odds do you accept?
I'm still slightly confused here myself. My initial thoughts were quite strongly in the 1/2 camp, but Arjun makes a compelling case.
Something that confuses me still more- what probability should Beauty ascribe, on waking, to the day being Tuesday? Is it 1/2, 1/3 or 1/4? 1/2 seems clearly wrong to me, but the original proposer of 1/3 seemed to think it correct.
* All experiments feature a Monday awakening. Half of experiments feature a Tuesday one. So Tuesday awakenings are exactly half as common as Monday ones. So the probability must be 1/3.
* There's a 50% chance of Heads, in which case it is Monday for sure. There's a 50% chance of Tails, in which case there's a 50% chance it's Tuesday. So the probability is 1/4.
If you ask me before the experiment, 'What is the probability of the coin landing heads conditional on you waking up as a sleeping beauty test subject,' 1/3. So I would not update throughout the experiment and still be a 'thirder'. If you just asked for the probability of the coin landing heads, I would say 1/2, and then me waking up and being interviewed would be evidence of the type 'I am a sleeping beauty test subject' and would cause me to update to 1/3.