There is an excellent piece in the New York Times by Jeremy W. Peters describing the outcome of last night’s (temporary) resolution to the debt ceiling and funding showdown. A quote stuck out at me:

Others could not explain why it took so much damage, to their party and the millions of people inconvenienced and worse by the shutdown, to end up right where so many of them expected.

Well, there is a simple MathOfPolitics explanation for this.  In a nutshell, it’s called a “pooling equilibrium” in game theory.  The classic example of this behavior is the “job market signaling model,” due to 2001 Nobel Laureate Michael Spence. The basic idea is that there are two types of workers/applicants: “low” type and “high” type, and employers would prefer to hire high type workers.  The type of a worker, however, is asymmetrically known: the worker knows his or her type, and the potential employer does not.  Rather, the employer can observe whether the applicant (say) went to college, and — here’s “the rabbit” — high types find college more enjoyable/less costly than low types.[1]  Employers see an applicant’s education (college or no college) and hire based on that information alone.  In the model, and this is key for the analogy, education is in and of itself inefficient—it does not make a worker better.  Rather, it is obtained in equilibrium only to the degree that it helps the worker in question procure employment.[2]

In every equilibrium of such a situation, the low type of worker does not obtain a degree unless the high type obtains one, too.  This leads, when the value of employment is sufficiently high, to both types of workers getting a degree, and thus the degree is observationally unimportant: some people with degrees get jobs, some don’t—degrees seem (observationally) to be unimportant.[3]

In other words, at the “beginning of the game” in such situations, everybody knows that getting a degree is “pointless,” and yet everybody knows that everybody will get it. In the end, applicants are hired with the same probability that they would have been if the option to get a degree were prohibited/taken off the table, and yet every applicant pays a positive cost to get the degree nonetheless.  Rephrasing:

The model explains why workers will get degrees to “get a job,” only to end up right where they started.

Here, the analogy is that “the Republicans” (it’s easy language, but see here) were trying to signal their “ideological purity/conservatism/belief in small government/hatred for the Affordable Care Act.”  In the end, the stakes for signaling this—say, successful circumvention of a primary challenge from a right-wing candidate—were perceived to be so large, relative to the costs of temporary shutdown and some briefly rattled markets that all (House) Republicans, regardless of their true beliefs/purity, were willing to go along with the gambit.  Note that this story is in line with the party line vote behind such procedural undergirdings of unity as discussed in this post, and, more math/less politics, is based on the counterfactual reasoning that drives signaling models discussed in this post.

So, to summarize: a simple signaling model not only explains what happened over the past 17+ days, it also offers an explanation for why what happened was foreseeable.  Thus, rephrasing one more time:

Game theory already explained and arguably predicted that it would take so much damage … to end up right where so many of them expected.

With that, I leave you with this.

__________

[1] When I say “the rabbit,” I mean (in layman’s terms) the causal mechanism: the thing that makes the model work, that explains the phenomenon that the model is aimed at, that makes the audience ultimately say “ahhhh!”

[2] And, no, I won’t admit that this is essentially a model of getting a PhD in the social sciences.  BECAUSE I (RE)LEARNED ABOUT POOLING EQUILIBRIA GETTING MY PhD.

[3] In a nontrivial set of cases (when employment is less valuable relative than the low type of worker’s net marginal cost of obtaining a degree relative to that experienced by the high type of worker), degrees are obtained only by high types, all applicants with degrees—and only those applicants—are employed, and degrees “look” valuable, even though they generate no inherent value on their own.  This is the first of many (empirically) important conclusions obtained by this deceptively simple model.