A really bad example, since they didn't tell you how much your life is worth to you.
It only changes what you'd pay proportionately, so it wouldn't make a difference.
The real problem is that they didn't tell you how much you're capable of paying. Let's assume you can pay an infinite amount. Perhaps they torture you for a period of time.
So, where does the author go wrong?
provided that you don't have heirs and all your remaining money magically disappears when you die.
Your money is only valuable if you survive. Think of it as them reducing your winnings. It doesn't matter if you don't win. In that case, you should be willing to have them reduce it by $333 in either case.
because they mix finite costs ($1000) in this case with infinite ones ("dead anyway", i.e. infinite loss)
If your utility function works like this, you can just abandon the finite part. It's effectively impossible for it to come up, and it's not really worth thinking about.
Also, you seemed to imply that it was a finite (though high) cost earlier.
The only time actually estimating cost comes into play is when the risk change is small enough to be close to the noise level.
Why would noise level matter?
A really bad example, since they didn't tell you how much your life is worth to you.
It only changes what you'd pay proportionately, so it wouldn't make a difference.
No, because, as you say:
The real problem is that they didn't tell you how much you're capable of paying.
I implied the same ("pay ALL I HAVE (and try to borrow some)"), if maybe not as succinctly.
...Your money is only valuable if you survive. Think of it as them reducing your winnings. It doesn't matter if you don't win. In that case, you should be willing to have them reduce
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?