While his purpose is to explain the monarchia of the Father and that the Father is the cause of the other two hypostases in the Trinity, Gregory, like every ancient thinker in the world, knew there was a direct causation between Theology and Society. What you believe about God determines what you believe about Government.
He originally writes
The three most ancient opinions concerning God are Anarchia, Polyarchia, and Monarchia. The first two are the sport of the children of Hellas, and may they continue to be so. For Anarchy is a thing without order; and the Rule of Many is factious, and thus anarchical, and thus disorderly. For both these tend to the same thing, namely disorder; and this to dissolution, for disorder is the first step to dissolution.
An astute observer could easily respond, “Yeah, and Gregory’s ultimate point is theology, not politics.” And that’s largely true, but Gregory is using the Greek word “Arche,” which means principle or origin both in the source of being and in the source of morality (government, social order). An error in the doctrine of the Trinity will determine the outflowing of the rest of social life. Interestingly, and from a other perspective, that’s also why Thomas Aquinas tied his belief in the Filioque with his strong doctrine of the Papacy.
***But Monarchy is that which we hold in honour. It is, however, a Monarchy that is not limited to one Person, for it is possible for Unity if at variance with itself to come into a condition of plurality; but one which is made of an equality of Nature and a Union of mind, and an identity of motion, and a convergence of its elements to unity— a thing which is impossible to the created nature— so that though numerically distinct there is no severance of Essence. Therefore Unity having from all eternity arrived by motion at Duality, found its rest in Trinity. This is what we mean by Father and Son and Holy Ghost. The Father is the Begetter and the Emitter; without passion of course, and without reference to time, and not in a corporeal manner. The Son is the Begotten, and the Holy Ghost the Emission; ***