The problem goes away if you allow a finite present value for immortality. In other words, there should be a probability level P(T) s.t. I am indifferent between living T periods with probability 1, and living infinitely with probability P(T). If immortality is infinitely valued, then you run into all sorts of ugly reducto ad absurdum arguments along the lines of the one outlined in your post.
In economics, we often represent expected utility as a discounted stream of future flow utilities. i.e.
V = Sum (B^t)(U_t)
In order for V to converge, we need B to be less than zero, and U_t to grow at rate less than 1/B for all t > T for some T. If a person with such a utility function were offered the deal described in the post above, they would at some point stop accepting. If you offered a better deal, they would accept for a while, but then stop again. If you continued this process, you would converge to the immortality case, and survival probability would converge to P.
Of course, this particular form is merely illustrative. Any utility function that assigns a finite value to immortality will lead to the same result.
The problem goes away if you allow a finite present value for immortality. In other words, there should be a probability level P(T) s.t. I am indifferent between living T periods with probability 1, and living infinitely with probability P(T). If immortality is infinitely valued, then you run into all sorts of ugly reducto ad absurdum arguments along the lines of the one outlined in your post.
In economics, we often represent expected utility as a discounted stream of future flow utilities. i.e.
V = Sum (B^t)(U_t)
In order for V to converge, we need B to be less than zero, and U_t to grow at rate less than 1/B for all t > T for some T. If a person with such a utility function were offered the deal described in the post above, they would at some point stop accepting. If you offered a better deal, they would accept for a while, but then stop again. If you continued this process, you would converge to the immortality case, and survival probability would converge to P.
Of course, this particular form is merely illustrative. Any utility function that assigns a finite value to immortality will lead to the same result.