In this experiment, like the standard Sleeping Beauty problem, a coin will be flipped and you will go to sleep.
If the coin shows Tails, you will be awoken on both Monday and Tuesday. Unlike the original problem, you will not be given any amnesia drug between Monday and Tuesday.
If the coin shows Heads, a die will be rolled. If the number is Even then you will be awoken on Monday only. If the number is Odd then you will be given false memories of having been previously awoken on Monday, but actually awoken only on Tuesday.
You wake up. You
(a) don’t remember waking up in this experiment before. What is your credence that the coin flip was Heads?
(b) remember waking up in this experiment before today. What is your credence that the coin flip was Heads?
Reasoning is the same as in the standard case: Probability (when used as a degree of belief) expresses the measure of your entanglement with a given hypothetical world. However, it is interesting that in both cases we know what day it is, making this a particularly evil version: Even after Beauty walks out of the experiment their credence still stays 1⁄3 indefinitely (given it wasn’t heads/even in which case beauty will know everything upon waking up on wednesday)!
Yet Another Sleeping Beauty variant
In this experiment, like the standard Sleeping Beauty problem, a coin will be flipped and you will go to sleep.
If the coin shows Tails, you will be awoken on both Monday and Tuesday. Unlike the original problem, you will not be given any amnesia drug between Monday and Tuesday.
If the coin shows Heads, a die will be rolled. If the number is Even then you will be awoken on Monday only. If the number is Odd then you will be given false memories of having been previously awoken on Monday, but actually awoken only on Tuesday.
You wake up. You
(a) don’t remember waking up in this experiment before. What is your credence that the coin flip was Heads?
(b) remember waking up in this experiment before today. What is your credence that the coin flip was Heads?
(a) 1⁄3 (b) 1⁄3
Reasoning is the same as in the standard case: Probability (when used as a degree of belief) expresses the measure of your entanglement with a given hypothetical world. However, it is interesting that in both cases we know what day it is, making this a particularly evil version: Even after Beauty walks out of the experiment their credence still stays 1⁄3 indefinitely (given it wasn’t heads/even in which case beauty will know everything upon waking up on wednesday)!