I'm still not sure that the reasoning is correct. It may depend on your life goals. For example, if your only goal in life is saving weasels from avalanches, which requires you to be alive but doesn't require any money, then case 2 lets you save 2x more future weasels than case 1, so I guess you'd pay more. On the other hand, if your utility function doesn't mention any weasels and you care only about candy bars eaten by the surviving version of you, then I'm not sure why you'd want to pay to survive at all. In either case Landsburg's conclusion seems to be wrong. Or am I missing something?
In the former case you'd pay infinity (or all you have) either way. In the latter case you'd pay zero either way. I don't see how that contradicts Landsburg.
Imagine you're playing Russian roulette. Case 1: a six-shooter contains four bullets, and you're asked how much you'll pay to remove one of them. Case 2: a six-shooter contains two bullets, and you're asked how much you'll pay to remove both of them. Steven Landsburg describes an argument by Richard Zeckhauser and Richard Jeffrey saying you should pay the same amount in both cases, provided that you don't have heirs and all your remaining money magically disappears when you die. What do you think?