I'm claiming that it is possible to define the utility function of any agent.
It is trivially possible to do that. Since no choice is strictly identical, you just add enough details to make each choice unique, and then choose a utility function that will always reach that choice
My formalism doesn't work like that since the utility function is a function over possible universes, not over possible choices. There is no trivial way to construct a utility function wrt which the given agent's intelligence is close to maximal. However it still might be the case we need to give larger weight to simple utility functions (otherwise we're left with selecting a maximum in an infinite set and it's not clear why it exists). As I said, I don't have the final formula.
A good simple model of human behaviour is that of different modules expressing preferences and short-circuiting the decision making in some circumstances, and a more rational system ("system 2") occasionally intervening to prevent loss through money pumps. So people are transitive in their ultimate decisions, often and to some extent, but their actual decisions depend strongly on which choices are presented first (ie their low level preferences are intransitive, but the rational part of them prevents loops). Would you say these beings have no preferences?
I'd say they have a utility function. Image a chess AI that selects moves by one of two strategies. The first strategy ("system 1") uses simple heuristics like "check when you can" that produce an answer quickly and save precious time. The second strategy ("system 2") runs a minimax algorithm with a 10-move deep search tree. Are all of the agent's decisions perfectly rational? No. Does it have a utility function? Yes: winning the game.
To construct a friendly AI, you need to be able to make vague concepts crystal clear, cutting reality at the joints when those joints are obscure and fractal - and them implement a system that implements that cut.
There are lots of suggestions on how to do this, and a lot of work in the area. But having been over the same turf again and again, it's possible we've got a bit stuck in a rut. So to generate new suggestions, I'm proposing that we look at a vaguely analogous but distinctly different question: how would you ban porn?
Suppose you're put in change of some government and/or legal system, and you need to ban pornography, and see that the ban is implemented. Pornography is the problem, not eroticism. So a lonely lower-class guy wanking off to "Fuck Slaves of the Caribbean XIV" in a Pussycat Theatre is completely off. But a middle-class couple experiencing a delicious frisson when they see a nude version of "Pirates of Penzance" at the Met is perfectly fine - commendable, even.
The distinction between the two case is certainly not easy to spell out, and many are reduced to saying the equivalent of "I know it when I see it" when defining pornography. In terms of AI, this is equivalent with "value loading": refining the AI's values through interactions with human decision makers, who answer questions about edge cases and examples and serve as "learned judges" for the AI's concepts. But suppose that approach was not available to you - what methods would you implement to distinguish between pornography and eroticism, and ban one but not the other? Sufficiently clear that a scriptwriter would know exactly what they need to cut or add to a movie in order to move it from one category to the other? What if the nude "Pirates of of Penzance" was at a Pussycat Theatre and "Fuck Slaves of the Caribbean XIV" was at the Met?
To get maximal creativity, it's best to ignore the ultimate aim of the exercise (to find inspirations for methods that could be adapted to AI) and just focus on the problem itself. Is it even possible to get a reasonable solution to this question - a question much simpler than designing a FAI?