I fail to see how this changes the answer to the St Petersburg paradox.
We have the option of 2 utility with 51% probability and 0 utility with 49% probability, and a second option of utility 1 with 100%.
Removing the worst 0.5% of the probability distribution gives us a probability of 48.5% for utility 0,
and removing the best 0.5% of the probability distribution gives us a probability of 50.5% for utility 2.
Renormalizing so that the probabilities sum to 1 gives us probabilities
97198 for utility 0, and 101198 for utility 2.
The expected value is then still greater than 1.
Thus we should choose the option where we have a chance at doubling utility.
I fail to see how this changes the answer to the St Petersburg paradox. We have the option of 2 utility with 51% probability and 0 utility with 49% probability, and a second option of utility 1 with 100%. Removing the worst 0.5% of the probability distribution gives us a probability of 48.5% for utility 0, and removing the best 0.5% of the probability distribution gives us a probability of 50.5% for utility 2. Renormalizing so that the probabilities sum to 1 gives us probabilities 97198 for utility 0, and 101198 for utility 2. The expected value is then still greater than 1. Thus we should choose the option where we have a chance at doubling utility.
Good point thanks for the comment. I’ll think about it some more and get back to you.
I posted a V2 of the post here: https://www.lesswrong.com/posts/WYGp9Kwd9FEjq4PKM/sbf-pascal-s-mugging-and-a-proposed-solution. I’m curious what do you think?
The new approach is to also incorporate (with more details in the post):
A bounded utility function to account for human indifference to changes in utility above or below a certain point.
A log or sub log utility function to account for human risk aversion.