The best approach I know for thinking about anthropic problems is Wei Dai's Updateless Decision Theory (UDT). We aren't yet able to solve all problems that we'd like to—for example, when it comes to game theory, the only games we have any idea how to solve are very symmetric ones—but for many anthropic problems, UDT gives the obviously correct solution. However, UDT is somewhat underspecified, and cousin_it's concrete models of UDT based on formal logic are rather heavyweight if all you want is to figure out the solution to a simple anthropic problem.

In this post, I introduce a toy decision theory, Simple Updateless Decision Theory or SUDT, which is most definitely not a replacement for UDT but makes it easy to formally model and solve the kind of anthropic problems that we usually apply UDT to. (And, of course, it gives the same solutions as UDT.) I'll illustrate this with a few examples.

This post is a bit boring, because all it does is to take a bit of math that we already implicitly use all the time when we apply updateless reasoning to anthropic problems, and spells it out in excruciating detail. If you're already well-versed in that sort of thing, you're not going to learn much from this post. The reason I'm posting it anyway is that there are things I want to say about updateless anthropics, with a bit of simple math here and there, and while the math may be intuitive, the best thing I can point to in terms of details are the posts on UDT, which contain lots of irrelevant complications. So the main purpose of this post is to save people from having to reverse-engineer the simple math of SUDT from the more complex / less well-specified math of UDT.

(I'll also argue that Psy-Kosh's non-anthropic problem is a type of counterfactual mugging, I'll use the concept of l-zombies to explain why UDT's response to this problem is correct, and I'll explain why this argument still works if there aren't any l-zombies.)

I'll introduce SUDT by way of a first example: the counterfactual mugging. In my preferred version, Omega appears to you and tells you that it has thrown a very biased coin, which had only a 1/1000 chance of landing heads; however, in this case, the coin has in fact fallen heads, which is why Omega is talking to you. It asks you to choose between two options, (H) and (T). If you choose (H), Omega will create a Friendly AI; if you choose (T...

Posts

Wikitag Contributions

Comments