The Shape of Possible States

Here is a working paper.

It's called "The Shape of Possible States," and it takes on two questions:

1. What does it mean to envision states as "like units," as is common in systemic theories of international politics?
2. Given an answer to (1), what are the criteria for an adequate model under the associated theoretical idiom?

I argue that the answer to (1) must be rooted in global analysis of the set of possible states, not just the ones we've seen. It's sort of Quinean in spirit: if our theories need to quantify over states, then we need to think hard about just what it is that's getting quantified over.

I conduct such a global analysis on the set of solutions to a simple force production problem. Waltz likens states to firms, so production is a straightforward entry point; Waltz and the bellicists in the state formation literature focus on the production of material power (or force). So, this seems like a good simple first cut.

And I find that the set of possible states so modeled is indeed (strikingly) similar: it's got a topological property called contractibility. This provides a "ladder of sameness:" four corollaries that provide increasingly-strong interpretations of just "how alike" the possible states are. The set of possibilities ignores:

1. Sorts (there are not two kinds of states in this model)
2. Transformations (any state can be turned into any other state)
3. Histories (any two paths linking common endpoints may be morphed into one another)
4. Information (any function defined on the set of states is homotopic to a constant, so there literally is no information in there other than "this holds the states.")

Taken together, these form a strong justification for like units assumptions in theoretical settings amenable to this first-cut of the state.

As for (2), I then show that the functions you might use to pin down a first-year-problem-set version of the force production problem (linear linear linear linear) adequately model the full space. My notion of adequacy is that of homotopy equivalence: we need the model to retain all structural properties of the mother space while (hopefully) providing a richer set of possibilities, too. (Or at least tractability!) The first-year-problem-set states are also contractible, but it turns out they also have a linear geometry evinced by their convexity as a set.

Anyway, it's a weird paper. Hopefully you enjoy it. Feel free to shoot me an email if you find any mistakes or have any criticisms to be addressed.