Perhaps the problem here is that you’re assuming that utility(probability, outcome) is the same as probability*utility(outcome).
If you don’t assume this, and calculate as if the utility of extra life decreased with the chance of getting it, the problem goes away,
since no amount of life will drive the probability down below a certain point. This matches intuition better, for me at least.
EDIT: What’s with the downvotes ?
In circumstances where the law of large numbers doesn’t apply, the utility of a probability of an outcome cannot be calculated from
just the probability and the utility of the outcome. So I suggested how the extra rule required might look.
Are the downvotes because people think this is wrong, or irrelevant to the question, or so trivial I shouldn’t have mentioned it ?
Perhaps the problem here is that you’re assuming that utility(probability, outcome) is the same as probability*utility(outcome). If you don’t assume this, and calculate as if the utility of extra life decreased with the chance of getting it, the problem goes away, since no amount of life will drive the probability down below a certain point. This matches intuition better, for me at least.
EDIT: What’s with the downvotes ?
In circumstances where the law of large numbers doesn’t apply, the utility of a probability of an outcome cannot be calculated from just the probability and the utility of the outcome. So I suggested how the extra rule required might look.
Are the downvotes because people think this is wrong, or irrelevant to the question, or so trivial I shouldn’t have mentioned it ?
I for one don’t follow your math; those 2 figures do look the same to me. Could you give some examples of how they give different answers?