An Agent Applies Rule Utilitarianism To The Universe
An Agent Applies Act Utilitarianism To The Universe
Case 1: Rule Utilitarianism Produces More Utility
In This Case, The Act Utilitarian's Optimal Action Would Be To Do Whatever A Rule Utilitarian Would Do.
This Results In Both Utilitarians Taking The Same Actions
Case 2: Act Utilitarianism Produces More Utility
In This Case, The Rule Utilitarian's Optimal Set Of Rules Would Contain Just One Rule -- To Do Whatever An Act Utilitarian Would Do.
This Results In Both Utilitarians Taking The Same Actions
Case 3: Both Utilitarians Produces The Same Utility
Therefore, Both Utilitarianisms Will Result In The Same Utility.