Your social welfare function produces a total preference ordering over outcomes, but not a mapping to real-numbered utilities. How do you decide between the median outcome and a 50% chance of either the best or worst? Do you plan to have the preference ordering be over probability distributions over outcomes?
The social welfare compromise varies with our ontology. If everyone agrees that two outcomes are the same, and therefore we represent them as the same outcome, it changes relative distances between preference orderings.
Nice catch. Yes, I think I’ll have to change the ordinal utility functions to range over lotteries rather than simply outcomes.
In this initial version, I am just assuming the ontology of the world is given, perhaps from just an oracle or the world model the AI has inferred.