Desirable properties that this may or may not have:
Partitioning the utilities, aggregating each component, then aggregating the results ought to not depend on the partition.
Any agent ought to want to submit its true utility function.
Taking the limit of introducing many copies of an indifferent utility into the mix recovers mean-max.
What happens when we use the resulting aggregated action as the new normalization pivot, and take a fixed point? The double-counting problem gets worse, but fixing it should also make this work.
If each agent can choose which action to submit to the random dictator policy, they might want to sacrifice a bit of their own utility (which they only currently want to improve their normalization position) in order to ruin other utilities (to worsen their normalization position). Two agents might cooperate by agreeing on an action they both submit.
In addition to the pivot each utility submits, we could take into account pivots selected by an aggregate of a subset of utilities. The full aggregate’s pivot would agree with what the others submit (due to the convergent instrumental goal of reflective consistency). This construction might be easy to make invariant under partitioning.
Desirable properties that this may or may not have:
Partitioning the utilities, aggregating each component, then aggregating the results ought to not depend on the partition.
Any agent ought to want to submit its true utility function.
Taking the limit of introducing many copies of an indifferent utility into the mix recovers mean-max.
What happens when we use the resulting aggregated action as the new normalization pivot, and take a fixed point? The double-counting problem gets worse, but fixing it should also make this work.
If each agent can choose which action to submit to the random dictator policy, they might want to sacrifice a bit of their own utility (which they only currently want to improve their normalization position) in order to ruin other utilities (to worsen their normalization position). Two agents might cooperate by agreeing on an action they both submit.
In addition to the pivot each utility submits, we could take into account pivots selected by an aggregate of a subset of utilities. The full aggregate’s pivot would agree with what the others submit (due to the convergent instrumental goal of reflective consistency). This construction might be easy to make invariant under partitioning.