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”.
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”.