## Mathematical models: why and what for?

An anthropologist friend of mine, Eli Thorkelson, recently asked for my comments on an article by feminist economist Julie Nelson. The article is a critique of rational choice theory (RCT) and I think it has some glaring omissions and misleading claims, but before I get to them I want to briefly offer the positive case for mathematical models, of which rational choice models are a subset.*

Markets and other social phenomena are complex.  We’re never going to have a theory that perfectly describes everything we might want to know about them.  Modeling is one way we can get some insight.  In a model we make some simplifying assumptions and then work out their implications.  Then, and this is key, we do empirical work; we analyze data to see how well our model captures various aspects of the phenomena we are interested in.  Ideally a  model will make predictions that are novel, in the sense that the researcher would not have made them before studying the model, and in the sense that they distinguish one model from another in a way that can be tested rigorously.

What about those simplifying assumptions?  If they turn out to be false, doesn’t that mean the model is junk?  Nope.  George Box famously said, “All models are wrong, but some are useful.”  If a model matches reality perfectly in some circumstances, but not so well in others, then we can simply use it where it works.  Newtonian physics, for example, is accurate enough for many engineering problems, but according to Einstein, Newton’s laws of motion are false.

In addition to accuracy, there are a number of other criteria by which models are evaluated.  For example, all else equal, simpler models are better because they are easier to understand (and some would argue, are more likely to be true).  More general models are also better, because they can be applied in more contexts and are subject to more stringent tests.

A lot of social scientists are hostile to mathematical models.  I think that one major reason for that is that they see the required unrealistic assumptions, and then dismiss the whole approach without studying them long enough to understand the value they provide.  Of course, formal modeling could never replace the primary forms of theorizing in psychology, sociology and anthropology, but with time I think more social scientists will come to see its strengths.

*To be clear, Eli has not endorsed the Nelson article, and has even dabbled in some mathematical modeling himself!

### 3 Responses to Mathematical models: why and what for?

1. Andrei Boutyline says:

I agree with your take on models, and also find it quite frustrating that there is so much confusion about them in sociology (I’ve found it useful to point out that concepts like class, race and gender, though clearly simplifying, still work fine in most contexts).

But with the specific context of the rational actor model, I am less sure–though I don’t want to jump to judgment. How much empirical validation has there been for it? It is clear that it fails to hold in many contexts. Are there some contexts in which it reliably works, or at least works well enough? How has this been validated? And does it usually only get applied to contexts for which it has been verified to hold?

2. Michael Bishop says:

I believe rational choice theory has proven useful in many areas, most notably, it forms the foundation of microeconomics. Of course, even if you agree with me that a lot of good work has been done with it, and think its important to point out the weaknesses of the models, or to argue that the dominance of RCT in economics has led to certain truths being overlooked, and we’d benefit from a greater diversity of modeling approaches.

I’d like to say a lot more about RCT, but it will come out over time in future blog posts.