The concept of the Trinity has helped me think through a number of issues related to the pollyty, two of which can be derived from the following drawing:
[First off, let me apologize to all Orthodox Christian readers for the filioque arrow. It is there only for historical, not ontological purposes, as i will explain below. For non-Christian readers, you are going to be totally lost.]
Just as the Father is the source of the divine essence and engenders the Son and spirates the Holy Spirit, so the State’s rule of law and the infrastructure it provides make Corporations (or broadly, Capitalism) and Pollyties possible. In that sense, both C and P are built on top of the social and political layer that is provided by S; and yet, insofar as the State’s legal infrastructure is used to define and maintain in existence both Corporations and Pollyties, it is tantamount to a shared essence or ousia: all three are institutions of some sort. But since they are fundamentally different kinds of institutions, and are defined against one another, they cannot be collapsed into one person or hypostasis. Just as the Father never incarnated, and the Son is not just a spirit, so the State is by definition not a voluntary association, and a corporation is not a democratic social net.
The second use i’ve made of the Trinitarian analogy is more basic. Historically, the third person of the Trinity (the Holy Spirit) emerged long (say, two centuries) after the Father and Son had been established as separate entities or persons. In fact, the Holy Spirit can be thought of as the necessary solution to the theological problems inherent in the “two God” approach (which seemed to inevitably degenerate into some kind of good god/bad god Gnosticism). The Holy Spirit brought balance to the godhead by serving as a liaison between the just heavenly Father and his earthly loving Son: like the Father, the Spirit was not human; like the Son, e proceeded from the Father; unlike either, e was never addressed in prayer. It is this harmony that made it possible to speak of one God in three persons. In the same way, the pollyty can be thought of as a placeholder for “whatever institution is needed to balance out states and corporations”. Any such institution will do.