By “power” I mean something like: the type of thing that helps a wide variety of agents pursue a wide variety of objectives in a given environment. For a more formal definition, see Turner et al (2020).
I think the draft tends to use the term power to point to an intuitive concept of power/influence (the thing that we expect a random agent to seek due to the instrumental convergence thesis). But I think the definition above (or at least the version in the cited paper) points to a different concept, because a random agent has a single objective (rather than an intrinsic goal of getting to a state that would be advantageous for many different objectives). Here's a relevant passage by Rohin Shah from the Alignment Newsletter (AN #78) pertaining to that definition of power:
You might think that optimal agents would provably seek out states with high power. However, this is not true. Consider a decision faced by high school students: should they take a gap year, or go directly to college? Let’s assume college is necessary for (100-ε)% of careers, but if you take a gap year, you could focus on the other ε% of careers or decide to go to college after the year. Then in the limit of farsightedness, taking a gap year leads to a more powerful state, since you can still achieve all of the careers, albeit slightly less efficiently for the college careers. However, if you know which career you want, then it is (100-ε)% likely that you go to college, so going to college is very strongly instrumentally convergent even though taking a gap year leads to a more powerful state.
[EDIT: I should note that I didn't understand the cited paper as originally published (my interpretation of the definition is based on an earlier version of this post). The first author has noted that the paper has been dramatically rewritten to the point of being a different paper, and I haven't gone over the new version yet, so my comment might not be relevant to it.]
I think using a well-chosen reward distribution is necessary, otherwise POWER depends on arbitrary choices in the design of the MDP's state graph. E.g. suppose the student in the above example writes about every action they take in a blog that no one reads, and we choose to include the content of the blog as part of the MDP state. This arbitrary choice effectively unrolls the state graph into a tree with a constant branching factor (+ self-loops in the terminal states) and we get that the POWER of all the states is equal.
I replied to this point with a short post.
I’ve written a draft report evaluating a version of the overall case for existential risk from misaligned AI, and taking an initial stab at quantifying the risk from this version of the threat. I’ve made the draft viewable as a public google doc here (Edit: arXiv version here, video presentation here, human-narrated audio version here). Feedback would be welcome.
This work is part of Open Philanthropy’s “Worldview Investigations” project. However, the draft reflects my personal (rough, unstable) views, not the “institutional views” of Open Philanthropy.