Intelligent Agent Foundations Forumsign up / log in
by Benja Fallenstein 1107 days ago | Patrick LaVictoire likes this | link | parent

Next, we consider the case that PA is consistent and work through the agent’s decision. PA can’t prove \(A()\neq1\), since we used the chicken rule, so since the sentence \(A()=1\to U()=5\) is easily provable, the sentence \(A()=1\to U()=10\) (ie. the first sentence that the agents checks for proofs of) must be unprovable.

It seems like this argument needs soundness of PA, not just consistency of PA. Do you see a way to prove in PA that if \(\mathrm{PA}\vdash A()\neq 1\), then PA is inconsistent?

[edited to add:] However, your idea reminds me of my post on the odd counterfactuals of playing chicken, and I think the example I gave there makes your idea go through:

The scenario is that you get 10 if you take action 1 and it’s not provable that you don’t take action 1; you get 5 if you take action 2; and you get 0 if you take action 1 and it’s provable that you don’t. Clearly you should take action 1, but I prove that modal UDT actually takes action 2. To do so, I show that PA proves \(A() = 1 \to \neg\square\ulcorner A() = 1\urcorner\). (Then from the outside, \(A() = 2\) follows from the outside by soundness of PA.)

This seems to make your argument go through if we can also show that PA doesn’t show \(A() \neq 1\). But if it did, then modal UDT would take action 1 because this comes first in its proof search, contradiction.

Thus, PA proves \(A() = 1 \to U() = 0\) (because this follows from \(A() = 1 \to \neg\square\ulcorner A() = 1\urcorner\)), and also PA doesn’t prove \(A() = 1 \to U() = 10\). As in your argument, then, the trolljecture implies that we should think “if the agent takes action 1, it gets utility 0” is a good counterfactual, and we don’t think that’s true.

Still interested in whether you can make your argument go through in your case as well, especially if you can use the chicken step in a way I’m not seeing yet. Like Patrick, I’d encourage you to develop this into a post.

by Sam Eisenstat 1107 days ago | Benja Fallenstein and Patrick LaVictoire like this | link

The argument that I had in mind was that if \(\rm{PA} \vdash \tt{A()} \ne 1\), then \(\rm{PA} \vdash \square \ulcorner \tt{A()} \ne 1 \urcorner\), so \(\rm{PA} \vdash \tt{A()} = 1\) since PA knows how the chicken rule works. This gives us \(\rm{PA} \vdash \bot\), so PA can prove that if \(\rm{PA} \vdash \tt{A()} \ne 1\), then PA is inconsistent. I’ll include this argument in my post, since you’re right that this was too big a jump.

Edit: We also need to use this argument to show that the modal UDT agent gets to the part where it iterates over utilities, rather than taking an action at the chicken rule step. I didn’t mention this explicitly, since I felt like I had seen it before often enough, but now I realize it is nontrivial enough to point out.






Note: I currently think that
by Jessica Taylor on Predicting HCH using expert advice | 0 likes

Counterfactual mugging
by Jessica Taylor on Doubts about Updatelessness | 0 likes

What do you mean by "in full
by David Krueger on Doubts about Updatelessness | 0 likes

It seems relatively plausible
by Paul Christiano on Maximally efficient agents will probably have an a... | 1 like

I think that in that case,
by Alex Appel on Smoking Lesion Steelman | 1 like

Two minor comments. First,
by Sam Eisenstat on No Constant Distribution Can be a Logical Inductor | 1 like

A: While that is a really
by Alex Appel on Musings on Exploration | 0 likes

> The true reason to do
by Jessica Taylor on Musings on Exploration | 0 likes

A few comments. Traps are
by Vadim Kosoy on Musings on Exploration | 1 like

I'm not convinced exploration
by Abram Demski on Musings on Exploration | 0 likes

Update: This isn't really an
by Alex Appel on A Difficulty With Density-Zero Exploration | 0 likes

If you drop the
by Alex Appel on Distributed Cooperation | 1 like

Cool! I'm happy to see this
by Abram Demski on Distributed Cooperation | 0 likes

Caveat: The version of EDT
by 258 on In memoryless Cartesian environments, every UDT po... | 2 likes

[Delegative Reinforcement
by Vadim Kosoy on Stable Pointers to Value II: Environmental Goals | 1 like


Privacy & Terms