In the case of finite trajectories, the objective function can be the sum of value functions across all states, with each state weighted equally—where states are types of observer-moments, and each state’s value function is its immediate valence plus the expected value of its continuations. This is total utilitarianism with two modifications. 1) aggregate over types instead of tokens, and 2) sum trajectory welfare instead of immediate welfare.
In the case of finite trajectories, the objective function can be the sum of value functions across all states, with each state weighted equally—where states are types of observer-moments, and each state’s value function is its immediate valence plus the expected value of its continuations. This is total utilitarianism with two modifications. 1) aggregate over types instead of tokens, and 2) sum trajectory welfare instead of immediate welfare.