I don’t see why owning other property would change the objective of having more gold. You are using gold to bet gold, where do other properties come into play? Nonetheless, if it bothers you just let’s just assume the subject has no other wealth other than what’s no him. Does that mean you still would not enter the bet?
The mad scientist does not need to lie. The experiment is changed to: 1. Sleep, 2.Scan, 3.Wake up the Orignal, 4. The original tosses the coin, 5. If tails create the Clone. 6. Wake up the Clone so he has indiscernible experience as the Orignal in 3. This whole process is disclosed to you. Now after waking up the coin may or may not have been tossed, what is the probability of Heads? What is the probability if you are the original? If you say they are both 1⁄2 then what is the probability that you are the clone?
Perhaps what confuses me the most is that you are arguing for both thirders and Halfers at the same time. If you think halfers are correct to say the probability of Heads is 1⁄2 wouldn’t you have taken the bet? If you think thirders are correct won’t you say the probability should be updated according to the standard Bayes rule? Why are you arguing against both of these? What’s your position?
If I am the original and have a job, house, 10000 gold in the bank, etc then I don’t need another 2 gold to buy shelter, food, etc. Being given 2 gold is vaguely nice, I can buy myself a nice book on decision theory or something. With 5 gold I could buy a book on decision theory and a concert ticket.
A duplicate with no legal claim to any property might need 2 gold to have a good chance to even survive. While 5 gold would give an even better chance of survival, only the original can win the extra 3 gold so risk-neutrality in the duplicate case is irrelevant.
If I’m unsure on whether or not I’m the duplicate, I’m not going to stake a nice book against years of life expectancy even if the odds were 100:1.
Now after waking up the coin may or may not have been tossed, what is the probability of Heads?
We’re using a model here analogous to the Sleeping Beauty 1⁄2 model right?
P(Heads | Observations upon awakening) = P(Heads) = 1⁄2 since the observations are stipulated to be identical and therefore independent of Heads.
What is the probability if you are the original?
That’s not actually an event in this space, and therefore has no measure. The measurable events in this space are just the sigma algebra generated by “Heads” and some set of possible “Observations on awakening”.
I don’t see why owning other property would change the objective of having more gold. You are using gold to bet gold, where do other properties come into play? Nonetheless, if it bothers you just let’s just assume the subject has no other wealth other than what’s no him. Does that mean you still would not enter the bet?
The mad scientist does not need to lie. The experiment is changed to: 1. Sleep, 2.Scan, 3.Wake up the Orignal, 4. The original tosses the coin, 5. If tails create the Clone. 6. Wake up the Clone so he has indiscernible experience as the Orignal in 3. This whole process is disclosed to you. Now after waking up the coin may or may not have been tossed, what is the probability of Heads? What is the probability if you are the original? If you say they are both 1⁄2 then what is the probability that you are the clone?
Perhaps what confuses me the most is that you are arguing for both thirders and Halfers at the same time. If you think halfers are correct to say the probability of Heads is 1⁄2 wouldn’t you have taken the bet? If you think thirders are correct won’t you say the probability should be updated according to the standard Bayes rule? Why are you arguing against both of these? What’s your position?
If I am the original and have a job, house, 10000 gold in the bank, etc then I don’t need another 2 gold to buy shelter, food, etc. Being given 2 gold is vaguely nice, I can buy myself a nice book on decision theory or something. With 5 gold I could buy a book on decision theory and a concert ticket.
A duplicate with no legal claim to any property might need 2 gold to have a good chance to even survive. While 5 gold would give an even better chance of survival, only the original can win the extra 3 gold so risk-neutrality in the duplicate case is irrelevant.
If I’m unsure on whether or not I’m the duplicate, I’m not going to stake a nice book against years of life expectancy even if the odds were 100:1.
We’re using a model here analogous to the Sleeping Beauty 1⁄2 model right?
P(Heads | Observations upon awakening) = P(Heads) = 1⁄2 since the observations are stipulated to be identical and therefore independent of Heads.
That’s not actually an event in this space, and therefore has no measure. The measurable events in this space are just the sigma algebra generated by “Heads” and some set of possible “Observations on awakening”.