A plan for Pascal's mugging?

yttrium

The idea is to compare not the results of actions, but the results of decision algorithms. The question that the agent should ask itself is thus:

"Suppose everyone¹ who runs the same thinking procedure like me uses decision algorithm X. What utility would I get at the 50th percentile (not: what expected utility should I get), after my life is finished?"
Then, he should of course look for the X that maximizes this value.

Now, if you formulate a turing-complete "decision algorithm", this heads into an infinite loop. But suppose that "decision algorithm" is defined as a huge table for lots of different possible situations, and the appropriate outputs.

Let's see what results such a thing should give:

If the agent has the possibility to play a gamble, and the probabilities involved are not small, and he expects to be allowed to play many gambles like this in the future, he should decide exactly as if he was maximizing expected utility: If he has made many decisions like this, he will get a positive utility difference in the 50th percentile if and only if his expected utility from playing the gamble is positive.
However, if Pascal's mugger comes along, he will decline: The complete probability of living in a universe where people like this mugger ought to be taken seriously is small. In the probability distribution over expected utility at the end of the agent's lifetime, the possibility of getting tortured will manifest itself only very slightly at the 50th percentile - much less than the possibility of losing 5 Dollars.

The reason why humans will intuitively decline to give money to the mugger might be similar: They imagine not the expected utility with both decisions, but the typical outcome of giving the mugger some money, versus declining to.

¹I say this to make agents of the same type cooperate in prisoner-like dilemmas.

The idea is to compare not the results of actions, but the results of decision algorithms. The question that the agent should ask itself is thus:

Let's see what results such a thing should give:

If the agent has the possibility to play a gamble, and the probabilities involved are not small, and he expects to be allowed to play many gambles like this in the future, he should decide exactly as if he was maximizing expected utility: If he has made many decisions like this, he will get a positive utility difference in the 50th percentile if and only if his expected utility from playing the gamble is positive.
However, if Pascal's mugger comes along, he will decline: The complete probability of living in a universe where people like this mugger ought to be taken seriously is small. In the probability distribution over expected utility at the end of the agent's lifetime, the possibility of getting tortured will manifest itself only very slightly at the 50th percentile - much less than the possibility of losing 5 Dollars.

¹I say this to make agents of the same type cooperate in prisoner-like dilemmas.

What happens if you're using this method and you're offered a gamble where you have a 49% chance of gaining 1000000utils and a 51% chance of losing 5utils (if you don't take the deal you gain and lose nothing). Isn't the "typical outcome" here a loss, even though we might really really want to take the gamble? Or have I misunderstood what you propose?

Depending on the rest of your utility distribution, that is probably true. Note, however, that an additional 10^6 utility in the right half of the utility function will change the median outcome of your "life": If 10^6 is larger than all the other utility you could ever receive, and you add a 49 % chance of receiving it, the 50th percentile utility after that should look like the 98th percentile utility before.

-2faul_sname14y

In such a case, the median outcome of all agents will be improved if every agent with the option to do so takes that offer, even if they are assured that it is a once/lifetime offer (because presumably there is variance of more than 5 utils between agents).