I think it would help a lot if you spelled out the premises more, because they’re quite opaque to me as written. E.g. I don’t know what “the norm reveals a choice function” means. (I think this kind of use of jargon without giving context is a common failure mode of current LLM summaries.)
I asked Claude to update the post to address your comment. There is now a section with the setup of the theorems, and clearer premises. Are they sufficiently understandable now?
Also, if I understand correctly, “behaviour maximizes a family of preference orderings...” means that the result only shows that we can represent an agent’s behavior as satisfying completeness.
I only briefly skimmed the article, but I agree with your interpretation. Claude agrees too.
The completeness here is a property of a ranking reconstructed from choices, and it comes almost entirely from premise 0: because the rule always names something acceptable, every pair gets settled. [This is now clarified in the section of the linkpost with the setup.] But the rule may name both options as acceptable, which the theorem records as the two being equally good — and that is also exactly how an agent who found them incomparable, and picked arbitrarily, would behave. The result therefore cannot distinguish “equally good” from “not comparable”, and so does not show that an agent deliberating about what to do must arrive at a complete ranking. It shows their behaviour is representable as if they had one.
Thanks, Anthony.
I asked Claude to update the post to address your comment. There is now a section with the setup of the theorems, and clearer premises. Are they sufficiently understandable now?
I only briefly skimmed the article, but I agree with your interpretation. Claude agrees too.