Why do theoreticians bother analyzing models with assumptions that are known to be false? And not just false in the sense of “only approximately true” but false in the sense of “not even close to true” or “we have no idea how true this is” or etc.? In particular, why do theoreticians bother with models that are false because they radically simplify reality?
This is something I’ve posted on a lot before (see list at end of post), and so have others. And it’s been discussed in the peer reviewed literature in ecology (e.g., Evans et al. in press). I’m bringing it up again because I just found two very good, contrasting pieces on this issue from economics. But even though they’re both from economics, neither one is very technical, or even specific to economics. They’re not only accessible, they’re good reads, and together they make a nice, thought-provoking pair.
First is an unpublished pre-print from Gilboa et al. (aside: sharing your unpublished pre-prints in order to get feedback is standard practice in economics and has been for decades) They suggest that models in economics be seen as case studies. The goal of modeling in economics isn’t to discover or derive general rules or laws (not even generalities that hold “all else being equal” or “approximately”), which is a contrast to physics. Instead, the goal is to develop “theoretical cases” which are analogous to empirical cases in some respect and so help us understand those empirical cases. This understanding can then be useful for purposes like prediction and management. On this view, models, observations, and experiments are all on an equal footing–they’re all cases that can be analogized directly to one another. I think this is relevant to ecology because I think simple models in ecology often are used the way models in economics are used.
Their argument here is actually distinct from (though related to) the familiar line that simple theoretical models “capture the essence” of the phenomenon and strip away unimportant details. It’s also distinct from (though related to) the familiar lines that simple models help to clarify one’s thinking, and identify otherwise-unrecognized possibilities. Gilboa et al.’s argument for the value of simple models provides an interesting counterpoint to the Evans et al. paper linked to above. Evans et al. argue that simple models aren’t general, nor are they explanatory (because they’re too abstract and not tied to any particular real-world system), and so can’t tell us much about any real-world system. Gilboa et al. agree that simple models don’t provide general rules or laws, although they do think simple models can be “general” in the sense of being analogous to many apparently-different empirical cases. But Gilboa et al. disagree that simple models aren’t explanatory or can’t inform us about particular real-world situations (for the record, I side with Gilboa et al. on this). Gilboa et al. also provides an interesting counterpoint to Tony Ives’ recent MacArthur award lecture. Like Gilboa et al., Tony sees theoretical models as providing a “library” of case studies which one can use to draw fruitful analogies between apparently-different cases. But in contrast to Gilboa et al., Tony’s “library” contains more in the way of system-specific models originally developed to address system-specific problems, rather than the sort of abstract, non-system-specific models Gilboa et al. discuss.
This brief summary doesn’t really do the paper justice–it’s much richer and more interesting than I can convey briefly. For instance, one bit that was new to me was their argument that simple models are to be preferred over complex ones not because simple models are more tractable, or because they’re closer to the truth, but because it’s easier to recognize analogies between simple situations than between complex situations.
Of course, analogies, valuable as they are, are tricky things. There are good and bad analogies, more and less precise analogies, etc. As Gilboa et al. themselves note, drawing an analogy between two distinct cases always involves judgment calls. Which is where the second piece comes in. In a recent blog post, economist Noah Smith notes the same differences between physics and economics in terms of how models are used. But Noah (whose background is in physics) bemoans this. He thinks that, in practice, the sort of analogy-making many (not all) economic theoreticians engage in just functions as a way to shield their models from proper testing. If the only thing we demand of economic models is that they be analogous to some real-world situation, that’s far too low a bar. In practice, the analogies are just too loose to help us either interpret the data or test the model. Plus, the math involved in economic models isn’t even elegant math, so doing economic modeling doesn’t provide the pure intellectual joy of doing elegant mathematics. I’m sure you can see how Noah’s worries might be applicable in ecology too.
I’m not going to try to adjudicate whether or when Gilboa et al. or Noah Smith (or both, or neither) is “right” in the context of ecology. Just wanted to throw them both out there as delicious and filling “food for thought”.
(HT Brad DeLong for pointing out Gilboa et al.)
Related posts:
False models are useful BECAUSE they’re false
R. A. Fisher vs. E. O. Wilson on math in biology
Theoreticians explain themselves to empiricists
Dynamic Ecology 
Simple models stand in their naked clarity in front of a reader, while too often unclear thinking hides behind “complexity.” What seems complex at first is often nothing but lazy thinking on the part of the modeler who did not bother to get to the core of the phenomena.