This post describes an infinite gamble that, under some reasonable assumptions, will motivate people who act to maximize an unbounded utility function to send me all their money. In other words, if you understand this post and it doesn't motivate you to send me all your money, then you have a bounded utility function, or perhaps even upon reflection you are not choosing your actions to maximize expected utility, or perhaps you found a flaw in this post.

Briefly, we do this with The St. Petersburg Paradox, converted to a mugging along the lines of Pascal's Mugging. I then tweaked it to extract all of the money instead of just a fixed sum.

I have always wondered if any actual payments have resulted from Pascal's Mugging, so I intend to track payments received for this variation. If anyone does have unbounded utility and wants to prove me wrong by sending money, send it with Paypal to tim at fungible dot com. Annotate the transfer with the phrase "St. Petersburg Mugging", and I'll edit this article periodically to say how much money I received. In order to avoid confusing the experiment, and to exercise my spite, I promise I will not spend the money on anything you will find especially valuable. SIAI would be better charity, if you want to do charity, but don't send that money to me.

Here's the hypothetical (that is, false) offer to persons with unbounded utility:

Let's call your utility function "UTILITY". We assume it takes a state of the universe as an argument.
Define DUT to be UTILITY(the present situation plus you receiving $1000)-UTILITY(the present situation). Here DUT stands for Difference in UTility. We assume DUT is positive.
You have unbounded utility, so for each nonnegative N there is a universe UN(N) such that UTILITY(UN(N)) is at least DUT * 2**N. Here UN stands for "universe".
The phrase "I am a god" is defined to mean that I am able to change the universe to any state I choose. I may not be a god after I make the change.
The offer is: For every dollar you send me, I will flip a coin. If it comes out Tails, or I am not a god, I will do nothing. If it comes out Heads and I am a god, I will flip the coin repeatedly until I see it come up Heads again. Let T be the number of times it was Tails. I will then change the universe to UN(T).

If I am lying and the offer is real, and I am a god, what utility will you receive from sending me a dollar? W...

NickHounsome

NickHounsome

NickHounsome

NickHounsome