Final answer:
The system of government introduced by Emperor Diocletian is known as the tetrarchy, a term derived from Greek that signifies rule by four emperors—two senior and two junior, which aimed to stabilize the Roman Empire during the Crisis of the Third Century.
Step-by-step explanation:
The term that best describes the system of government that Emperor Diocletian tried to establish is tetrarchy. Diocletian divided the Roman Empire between four rulers, creating a unique form of governance where power was shared amongst two senior emperors, titled Augustus, and two junior emperors, titled Caesar. The tetrarchy was meant to end the cycle of assassinations and provide an orderly succession, as junior emperors were designated heirs of the senior emperors. The system functioned to quell the Crisis of the Third Century, stabilizing the empire during Diocletian's reign though it eventually failed after his death leading to civil war and the eventual rise of Emperor Constantine as the sole ruler.