Sleeping Beauty is an edge case where different reward structures are intuitively possible, and so people imagine different game payout structures behind the definition of “probability”. Once the payout structure is fixed, the confusion is gone. With a fixed payout structure&preference framework rewarding the number you output as “probability”, people don’t have a disagreement about what is the best number to output. Sleeping beauty is about definitions.)
And still, I see posts arguing that if a tree falls on a deaf Sleeping Beauty, in a forest with no one to hear it, it surely doesn’t produce a sound, because here’s how humans perceive sounds, which is the definition of a sound, and there are demonstrably no humans around the tree. (Or maybe that it surely produces the sound because here’s the physics of the sound waves, and the tree surely abides by the laws of physics, and there are demonstrably sound waves.)
This is arguing about definitions. You feel strongly that “probability” is that thing that triggers the “probability” concept neuron in your brain. If people have a different concept triggering “this is probability”, you feel like they must be wrong, because they’re pointing at something they say is a sound and you say isn’t.
Probability is something defined in math by necessity. There’s only one way to do it to not get exploited in natural betting schemes/reward structures that everyone accepts when there are no anthropics involved. But if there are multiple copies of the agent, there’s no longer a single possible betting scheme defining a single possible “probability”, and people draw the boundary/generalise differently in this situation.
You all should just call these two probabilities two different words instead of arguing which one is the correct definition for “probability”.
People are arguing about the answer to the Sleeping Beauty! I thought this was pretty much dissolved with this post’s title! But there are lengthy posts and even a prediction market!
Sleeping Beauty is an edge case where different reward structures are intuitively possible, and so people imagine different game payout structures behind the definition of “probability”. Once the payout structure is fixed, the confusion is gone. With a fixed payout structure&preference framework rewarding the number you output as “probability”, people don’t have a disagreement about what is the best number to output. Sleeping beauty is about definitions.)
And still, I see posts arguing that if a tree falls on a deaf Sleeping Beauty, in a forest with no one to hear it, it surely doesn’t produce a sound, because here’s how humans perceive sounds, which is the definition of a sound, and there are demonstrably no humans around the tree. (Or maybe that it surely produces the sound because here’s the physics of the sound waves, and the tree surely abides by the laws of physics, and there are demonstrably sound waves.)
This is arguing about definitions. You feel strongly that “probability” is that thing that triggers the “probability” concept neuron in your brain. If people have a different concept triggering “this is probability”, you feel like they must be wrong, because they’re pointing at something they say is a sound and you say isn’t.
Probability is something defined in math by necessity. There’s only one way to do it to not get exploited in natural betting schemes/reward structures that everyone accepts when there are no anthropics involved. But if there are multiple copies of the agent, there’s no longer a single possible betting scheme defining a single possible “probability”, and people draw the boundary/generalise differently in this situation.
You all should just call these two probabilities two different words instead of arguing which one is the correct definition for “probability”.