It should be clear that I can engineer a situation where survival <==> winning the lottery, in which case I am indifferent between (winning the lottery and not dying) and (not dying) because they occur in approximately the same set of possible worlds.
That doesn’t follow unless, in the beginning, you were already indifferent between (winning the lottery and not dying) and (dying). Remember, a utility function is a map from all possible states of the world to the real line (ignore what economists do with utility functions for the moment). (being alive) is one possible state of the world. (being alive and having won the lottery) is not the same state of the world. In more detail, assign arbitrary numbers for utlity (aside from rank) - suppose U(being alive) = U(being dead) = 0 and suppose U(being alive and having won the lottery) = 1.
Now you engineer the situation such that survival <==> having won the lottery. It is still the case that U(survival) = 0. Your utility function doesn’t change because some random aspect of reality changes—if you evaluate the utility of a certain situation at time t, you should get the same answer at time t+1. It’s still the same map from states of the world to the real line. A terse way of saying this is “when you ask the question doesn’t change the answer.” But if we update on the fact that survival ⇒ having won the lottery, then we know we should really be asking about U(being alive and having won the lottery) which we know to be 1, which is not the same as U(dying).
That doesn’t follow unless, in the beginning, you were already indifferent between (winning the lottery and not dying) and (dying). Remember, a utility function is a map from all possible states of the world to the real line (ignore what economists do with utility functions for the moment). (being alive) is one possible state of the world. (being alive and having won the lottery) is not the same state of the world. In more detail, assign arbitrary numbers for utlity (aside from rank) - suppose U(being alive) = U(being dead) = 0 and suppose U(being alive and having won the lottery) = 1.
Now you engineer the situation such that survival <==> having won the lottery. It is still the case that U(survival) = 0. Your utility function doesn’t change because some random aspect of reality changes—if you evaluate the utility of a certain situation at time t, you should get the same answer at time t+1. It’s still the same map from states of the world to the real line. A terse way of saying this is “when you ask the question doesn’t change the answer.” But if we update on the fact that survival ⇒ having won the lottery, then we know we should really be asking about U(being alive and having won the lottery) which we know to be 1, which is not the same as U(dying).