Josh von Korff, a physics grad student here at Berkeley, and versions of Newcomb’s problem. He shared my general intuition that one should choose only one box in the standard version of Newcomb’s problem, but that one should smoke in the smoking lesion example. However, he took this intuition seriously enough that he was able to come up with a decision-theoretic protocol that actually seems to make these recommendations. It ends up making some other really strange predictions, but it seems interesting to consider, and also ends up resembling something Kantian!
The basic idea is that right now, I should plan all my future decisions in such a way that they maximize my expected utility right now, and stick to those decisions. In some sense, this policy obviously has the highest expectation overall, because of how it’s designed.
Korff also reinvents counterfactual mugging:
Here’s another situation that Josh described that started to make things seem a little more weird. In Ancient Greece, while wandering on the road, every day one either encounters a beggar or a god. If one encounters a beggar, then one can choose to either give the beggar a penny or not. But if one encounters a god, then the god will give one a gold coin iff, had there been a beggar instead, one would have given a penny. On encountering a beggar, it now seems intuitive that (speaking only out of self-interest), one shouldn’t give the penny. But (assuming that gods and beggars are randomly encountered with some middling probability distribution) the decision protocol outlined above recommends giving the penny anyway.
In a sense, what’s happening here is that I’m giving the penny in the actual world, so that my closest counterpart that runs into a god will receive a gold coin. It seems very odd to behave like this, but from the point of view before I know whether or not I’ll encounter a god, this seems to be the best overall plan. But as Josh points out, if this was the only way people got food, then people would see that the generous were doing well, and generosity would spread quickly.
And he looks into generalizing to the algorithmic version:
If we now imagine a multi-agent situation, we can get even stronger (and perhaps stranger) results. If two agents are playing in a prisoner’s dilemma, and they have common knowledge that they are both following this decision protocol, then it looks like they should both cooperate. In general, if this decision protocol is somehow constitutive of rationality, then rational agents should always act according to a maxim that they can intend (consistently with their goals) to be followed by all rational agents. To get either of these conclusions, one has to condition one’s expectations on the proposition that other agents following this procedure will arrive at the same choices.
Philosopher Kenny Easwaran reported in 2007 that:
Korff also reinvents counterfactual mugging:
And he looks into generalizing to the algorithmic version:
Korff is now an Asst. Prof. at Georgie State.
If it’s an iterated game, then the decision to pay is a lot less unintuitive.