Final answer:
The system of government attempted by Emperor Diocletian is known as the tetrarchy, aimed at stabilizing the Roman Empire by dividing rule among four emperors. Despite temporary success, the system swiftly faltered after Diocletian's retirement and ended with Constantine the Great's reunification of the empire.
Step-by-step explanation:
The term that best describes the system of government Emperor Diocletian tried to establish is tetrarchy, which is Greek for rule by four. Diocletian's innovation, the Tetrarchy, consisted of two senior emperors (augusti) and two junior emperors (caesars), each pair controlling either the eastern or western portion of the Roman Empire. This system was put into place to bring stability to an empire suffering from internal strife and external threats, hoping to end the cycle of assassinations by having a peaceful succession system where juniors would become seniors and then select new juniors.
Under Diocletian, the empire also underwent financial and administrative reforms, such as tax realignment and the division into smaller provinces for better governance. Despite the initial success, the Tetrarchy system only functioned as intended once; after Diocletian's retirement in 305 CE and following his co-emperor's reluctant stepping down, the empire fell back into civil war, and it was not until Constantine the Great that the empire was reunified under a single ruler.