post by [deleted] · · ? · GW · 0 comments

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comment by shminux · 2022-11-16T04:30:07.553Z · LW(p) · GW(p)

"it all disappears" has a negative infinity value, so the game is never worth playing. In the St.Peterburg paradox you lose money. In the proposed setup you lose everything for everyone. 

comment by harfe · 2022-11-16T04:01:39.625Z · LW(p) · GW(p)

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 gives us probabilities for utility , and for utility . The expected value is then still greater than . Thus we should choose the option where we have a chance at doubling utility.

Replies from: cole-killian, cole-killian
comment by Cole Killian (cole-killian) · 2022-11-16T22:20:08.405Z · LW(p) · GW(p)

Good point thanks for the comment. I'll think about it some more and get back to you.

comment by Cole Killian (cole-killian) · 2022-11-18T18:42:21.682Z · LW(p) · GW(p)

I posted a V2 of the post here: [LW · GW]. 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.