Most concern about AI comes down to the scariness of goal-oriented behavior. A common response to such concerns is “why would we give an AI goals anyway?” I think there are good reasons to expect goal-oriented behavior, and I’ve been on that side of a lot of arguments. But I don’t think the issue is settled, and it might be possible to get better outcomes without them. I flesh out one possible alternative here, based on the dictum "take the action I would like best" rather than "achieve the outcome I would like best."
(As an experiment I wrote the post on medium, so that it is easier to provide sentence-level feedback, especially feedback on writing or low-level comments.)
What "a single time step" means here depends on what model Arthur learns, which may not be what we intend. For example, suppose a is an action which immediately disables the approval input terminal or the data connection between Arthur and the terminal via a network attack, then taking an arbitrarily long time to secure access to the approval input terminal and giving itself maximum approval. What is approval[T][a] according to Arthur's model?
Overall, don't you think it's too strong to say "But unlike AIXI, Arthur will make no effort to manipulate these judgments." even if Arthur, like short-sighted AIXI, is safer than standard AIXI? As another example, suppose Arthur discovers some sort of flaw in human psychology which lets it manipulate whoever is going to enter the next approval value into giving it maximum approval. Wouldn't Arthur take advantage of that?