More by training than for any sense of conviction, I belong to the rat choice and quant camp. My training as an economist gave me a set of analytical tools, which I use as often as I can to make sense of the world. A lot of things remain beyond the grasp of those tools--but they are helpful tools on any case.
Every now and then I face four kinds of charges--actually, so often that I almost have instant replies. Let's see:
1. They (we) are irrational! Your ratchoice models are useless because people are not/not always/not very rational.
Granted, for every definition of rationality you have one can find 100 people behaving irrationally. My preferred definition of rationality implies either cost-minimizing or consistent (ie, transitive) behavior or both. But the strength of the rationality assumption and that of ratchoice theories is a matter of a) degree and b) consistency.
Degree: As long as people behave relatively more in cost-minimizing ways than in haphazard ways, rat choice models will be useful to explain such behavior. Consistency: even if we admit/assume that people are irrational, any decent explanation of such behavior has to be consistent/logic/rational. If not, how could you distinguish between an "irrational theory" of any behavior and a "bogus/just-so" story about that same behavior?
Actually, a favorite hobby of mine is to read or listen supposedly anti-rat choice people offer their theories and evidence, and then try to find the devilish little ratchoice model implicit in their argumentation... and guess what, it is always there more often than you (or they) think.
The typical shape of the anti-rat choice argument goes like this: "well, ratchoice theory A predicts outcome Y1... but as it turns out outcome Y2 ocurred, why? Because silly-theory A neglected the role of key missing/unobservable variable X. Once you consider my theory, which includes a subjective/qualitative valuation of variable X, it is obvious that outcome Y2 had to occur..." What this line of argument forgets to mention is that "ratchoice theory A + mysterious variable X" (call it theory A') still is (or can be construed as) a ratchoice theory.
I am NOT saying that any theory is a ratchoice theory, just that a lot of supposedly non-ratchoice theories are actually pretty close to ratchoice theories--with different keywords and no equations. The fear of using mathematical or even functional language to make theoretical arguments is dumbfounded: math is just another language, a strict and picky one indeed. Some arguments are easier to make with math and some others with prose... but they are not mutually excludable. Ok, there is an exception: it is easier to spot logical inconsistencies in a simple math model than in a 100 page narrative.
An extreme version is harder to tackle: "See, people are irrational, hence the world is unpredictable. Want evidence? Just look how Y1 happens sometimes while Y2 also happens other times! I am telling you those ratchoice empiricists know nothing!" The most extreme case: "Why are you so deterministic? Why do you want to explain anything at all to begin with?" I have not figured out a reply to any of these...
These are the other three typical charges:
1) It's a qualitative-world! Your quantitative methods are useless because not everything is measurable nor observable.
Quick reply: Granted, everything is up for grabs in the quali-land. But why should I give more credit to your subjective interpretation of the world than the one you give to my subjective choice of variables to measure it?
3) Nothing new! Ok, you measured something but you are only proving something that "everybody knew already".
Quick reply: I am pleased that my findings corroborate your priors, and I hope you update them accordingly. By the way, did you have an estimate of the magnitude of this impact in this particular context too? Did you know the particular cases where this correlation does/does not hold? I didn't before, but I do now.
4) No causality! Ok, you found a significant correlation but you have not demonstrated causality.
Quick reply: Stats will never prove causality--that is not its job. Sensible theory + evidence based on decent research design = closer to causality. What is your rival theory? What kind of evidence would you like to see to convince you? Is that evidence feasible at reasonable cost? Do you apply those same standards to your own work?