Both Aristotle and Aquinas seem to subscribe to the idea of a mixed constitution as the form of government best disposed to the common good. By "mixed constitution", I mean mixing between Aristotle's classical taxonomy of political government (Kingship, Oligarchy, Democracy). I wonder how do their ideas of "mixed government" differ? For example, for Aristotle in Politics, the mixing is actually to find a mean between the extremes. So he builds his best constitution on the metaphysics of "middle class," which is the mean of the rich and poor. This is not the case in summa theologica by Aquinas, who just chooses one characteristic from each good form of government and combines them. Are there any other dissimilarities between the two? E.g., we all know that Aquinas tries to adapt Aristotlean philosophy to Christian theology. So what role does theology play in Aquinas' mixed government different from that of Aristotle's?
Integralism: A Manual of Poilitical Philosophy ch. 5 "Forms of Polity", §"Possibility of mixed polities":
Aristotle noted that “some say that the best constitution is a mixture of all the constitutions (την άρίστην πολιτείαν εξ άπασών είναι των πολιτειών μεμειγμένην)”.[Politics II.6] The phrase however has been variously used, sometimes to refer to a constitution giving a stake in the city to all the social classes, sometimes to refer to a separation of the organs of government. Here we use it to refer to a polity which possesses elements of more than one of the three ‘pure’ polities. This yields four new possibilities: a mixture of all three pure polities, a mixture of monarchy and aristocracy, of monarchy and democracy, and of aristocracy and democracy. Hence we may speak of seven basic forms of polity, as St Robert Bellarmine remarks [in On the Roman Pontiff bk. 1 ch. 1].
St. Thomas in De Regno ch. 4 agrees with Aristotle that tyranny, oligarchy, and democracy are corruptions of monarchy, aristocracy, and timocracy*, respectively:
democracy stands in contrary opposition to polity*, since both are governments carried on by many persons, […]; while oligarchy is the opposite of aristocracy, since both are governments carried on by a few persons; and kingship is the opposite of tyranny since both are carried on by one person.
*Integralism ibid. fn. 5: "In the Nicomachean Ethics, VIII.10, Aristotle explains that this word comes from the term τίμημα (timeema), property, and denotes rule by many people who nevertheless each possess a specified amount of property. He notes that such a system is normally called by the name of the genus, and termed a ‘polity’. In the Politics, he conforms to this common but confusing practice."
Although a theological work, St. Thomas Aquinas does describe the ideal form of government in Summa Theologica I-II q. 105 a. 1 ("Whether the Old Law enjoined fitting precepts concerning rulers?") co.:
the first place is held by the "kingdom," where the power of government is vested in one; and "aristocracy," which signifies government by the best, where the power of government is vested in a few. Accordingly, the best form of government is in a state or kingdom, where one is given the power to preside over all; while under him are others having governing powers: and yet a government of this kind is shared by all, both because all are eligible to govern, and because the rules are chosen by all. For this is the best form of polity, being partly kingdom, since there is one at the head of all; partly aristocracy, in so far as a number of persons are set in authority; partly democracy, i.e. government by the people, in so far as the rulers can be chosen from the people, and the people have the right to choose their rulers.