I have no reason to select you as a likely god candidate, compared to the ~infinite number of people who exist across all of space-time and all Everett branches.
Agreed. However, you also have no reason to carry on your business dealing with ordinary things rather than focusing exclusively on the various unlikely gods that might be trying to jerk you around. I don't win, but you lose.
2b) Even if you flip coins incredibly fast and in parallel, I will still eventually die, so we can only count the number of coin flips that happen before then.
Yes, I forgot to mention that if I'm a god I can stop time while I'm flipping coins.
Assume a utility function which is finite but unbounded. It cannot handle infinity, and thus your mugging relies on an invalid input (infinite utility), and is discarded as malformed.
If you play by those rules, you can't assign a utility to the infinite gamble, so you can't make decisions about it. If the infinite gamble is possible, your utility function is failing to do its job, which is to help you make decisions. Tell me how you want to fix that without bounded utility.
my mind assigns p(you are god) = "bullshit, prove it", and this is about the closest I can come to expressing that mathematically
p(I am god) = 0 is simpler and gets the job done. That appears to be more restrictive than the Universal Prior -- I think the universal prior would give positive probability to me being god. There might be a general solution here to specifying a prior that doesn't fall into these pits, but I don't know what it is. Do you?
Assign probabilities by frequency of occurrence. There have been no instances of god yet, so p(god) = 0. Once god has been demonstrated, I can update off of this 0, unlike with Bayesian statistics.
How would this work in general? How could you plan for landing on the moon if it hasn't been done before? You need to distinguish "failure is certain because we put a large bomb in the rocket that will blow up before it gets anywhere" from "failure is certain because it hasn't been done before and thus p(success) = 0".
you also have no reason to carry on your business dealing with ordinary things
Yes I do. Dealing with ordinary things has a positive expected utility. Analysing anything that looks like a Pascal's Mugging has ~zero expected utility as far as the wager itself goes, plus that derived from curiosity and a desire to study logical problems. I believe that Counterargument #5 can be tuned and expanded to apply to all such muggings, so I'll be writing that up in a bit :)
p(I am god) = 0 is simpler and gets the job done
Assuming Bayesian probability, p=0 means ...
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:
If I am lying and the offer is real, and I am a god, what utility will you receive from sending me a dollar? Well, the probability of me seeing N Tails followed by a Head is (1/2)**(N + 1), and your utility for the resulting universe is UTILITY(UN(N)) >= DUT * 2**N, so your expected utility if I see N tails is (1/2)**(N + 1) * UTILITY(UN(N)) >= (1/2)**(N + 1) * DUT * 2 ** N = DUT/2. There are infinitely many possible values for N, so your total expected utility is positive infinity * DUT/2, which is positive infinity.
I hope we agree that it is unlikely that I am a god, but it's consistent with what you have observed so far, so unless you were born with certain knowledge that I am not a god, you have to assign positive probability to it. Similarly, the probability that I'm lying and the above offer is real is also positive. The product of two positive numbers is positive. Combining this with the result from the previous paragraph, your expected utility from sending me a dollar is infinitely positive.
If you send me one dollar, there will probably be no result. Perhaps I am a god, and the above offer is real, but I didn't do anything beyond flipping the first coin because it came out Tails. In that case, nothing happens. Your expected utility for the next dollar is also infinitely positive, so you should send the next dollar too. By induction you should send me all your dollars.
If you don't send money because you have bounded utility, that's my desired outcome. If you do feel motivated to send me money, well, I suppose I lost the argument. Remember to send all of it, and remember that you can always send me more later.
As of 7 June 2011, nobody has sent me any money for this.
ETA: Some interesting issues keep coming up. I'll put them here to decrease the redundancy: