I also reject the claim that C and B are equivalent (unless the utility of survival is 0, +infinity, or -infinity). If I accepted their line of argument, then I would also have to answer the following set of questions with a single answer.
Question E: Given that you’re playing Russian Roulette with a full 100-shooter, how much would you pay to remove all 100 of the bullets?
Question F: Given that you’re playing Russian Roulette with a full 1-shooter, how much would you pay to remove the bullet?
Question G: With 99% certainty, you will be executed. With 1% certainty you will be forced to play Russian Roulette with a full 1-shooter. How much would you pay to remove the bullet?
Question H: Given that you’re playing Russian Roulette with a full 100-shooter, how much would you pay to remove one of the bullets?
You reject the claim, but can you point out a flaw in their argument?
I claim that the answers to E, F, and G should indeed be the same, but H is not equivalent to them. This should be intuitive. Their line of argument does not claim H is equivalent to E/F/G—do the math out and you’ll see.
Actually my revised opinion, as expressed in my reply to Tyrell_McAllister, is that the authors’ analysis is correct given the highly unlikely set-up. In a more realistic scenario, I accept the equivalences A~B and C~D, but not B~C.
I claim that the answers to E, F, and G should indeed be the same, but H is not equivalent to them. This should be intuitive. Their line of argument does not claim H is equivalent to E/F/G—do the math out and you’ll see.
I really don’t know what you have in mind here. Do you also claim that cases A, B, C are equivalent to each other but not to D?
After further reflection, I want to say that the problem is wrong (and several other commenters have said something similar): the premise that your money buys you no expected utility post mortem is generally incompatible with your survival having finite positive utility.
Your calculation is of course correct insofar as it stays within the scope of the problem. But note that it goes through exactly the same for my cases F and G. There you’ll end up paying iff X ≤ L, and thus you’ll pay the same amount to remove just 1 bullet from a full 100-shooter as to remove all 100 of them.
I also reject the claim that C and B are equivalent (unless the utility of survival is 0, +infinity, or -infinity). If I accepted their line of argument, then I would also have to answer the following set of questions with a single answer.
Question E: Given that you’re playing Russian Roulette with a full 100-shooter, how much would you pay to remove all 100 of the bullets?
Question F: Given that you’re playing Russian Roulette with a full 1-shooter, how much would you pay to remove the bullet?
Question G: With 99% certainty, you will be executed. With 1% certainty you will be forced to play Russian Roulette with a full 1-shooter. How much would you pay to remove the bullet?
Question H: Given that you’re playing Russian Roulette with a full 100-shooter, how much would you pay to remove one of the bullets?
You reject the claim, but can you point out a flaw in their argument?
I claim that the answers to E, F, and G should indeed be the same, but H is not equivalent to them. This should be intuitive. Their line of argument does not claim H is equivalent to E/F/G—do the math out and you’ll see.
Actually my revised opinion, as expressed in my reply to Tyrell_McAllister, is that the authors’ analysis is correct given the highly unlikely set-up. In a more realistic scenario, I accept the equivalences A~B and C~D, but not B~C.
I really don’t know what you have in mind here. Do you also claim that cases A, B, C are equivalent to each other but not to D?
Oops, sorry! I misread. My bad. I would agree that they are all equivalent.
What do you make of my argument here?
After further reflection, I want to say that the problem is wrong (and several other commenters have said something similar): the premise that your money buys you no expected utility post mortem is generally incompatible with your survival having finite positive utility.
Your calculation is of course correct insofar as it stays within the scope of the problem. But note that it goes through exactly the same for my cases F and G. There you’ll end up paying iff X ≤ L, and thus you’ll pay the same amount to remove just 1 bullet from a full 100-shooter as to remove all 100 of them.