The scientific community has a strong bias in favour of theoretical rigour. This is shared in social science. Economists especially tend to believe that theories ought to be precise, and if possible, written in maths. Many would even say something stronger: an imprecise theory is not really a theory at all. It's just verbal fluff.
This is wrong. Vague theories are useful. What is more, formal theories can be vague.
Here are two useful but vague theories. The first is LOFTY theory. This is advanced by the first mate of an aircraft carrier, to the captain, during navigation into a busy port. LOFTY derives its name from the theory's single empirical claim:
(1) Look Out For That Yacht!
This is clearly vague. A rigorous response would be:
"Sorry, but what exactly is a yacht? Wikipedia states that it is a recreational boat or ship, either a sailing or power boat. But the definition of recreation is itself loose. For example, a river cruiser full of tourists – is that a yacht? Surely some smaller recreational sailing boats would be called dinghies, not yachts. On the other hand, at larger sizes the same article admits that 'the distinction between yacht and ship becomes blurred'. Besides, even if yacht is well-defined in terms of the current universe of sailing vessels, I can easily imagine possible vessels that might thoroughly blur the edges of the category. I'm really not sure what you are saying."
Yet, the theory seems useful, and the captain's response is ill-advised.
My second example is Just World Theory from psychology. This claims that people are motivated to believe that the world is a fair place, and that therefore misfortune must be deserved. For example, people with strong beliefs in a just world were more favourable to those who received a "good" number in the Vietnam draft lottery than to those who got a "bad" number.
Just World Theory is vague. It seems vulnerable to the 1-800 critique (Al Roth once suggested that psychologists should add a 1-800 number to their theory papers, so that other scientists can call them up and ask them whether their theory applies in a particular case). In many cases, people are motivated to redress injustice, and sympathetic to losers, so when exactly does JWT kick in? We also don't know exactly what counts as misfortune, or what counts as fairness.
Yet, I submit, Just World Theory is useful. It organizes a lot of data. And, because of its vagueness, it is available for researchers trying to understand behaviour in many different contexts.
I don't say we shouldn't try to make theories more precise. Psychologists are constantly trying to do that. Rigour is good. But it is not a prerequisite. Many theories are interesting before they become precise. Some theories may be very hard ever to make precise, but they may still be useful – we might even want to say "true".
The point is relevant to behavioural economics. Arguably, behaviouralists reach for formal models too quickly. For instance, elegant formalizations of social preferences are often contradicted by subsequent experiments; I suspect they could have been "disproved" by simple thought experiment. (You might estimate large altruism parameters from dictator games; but a priori, most people don't give half their income away.)
My second point is that formal models are often, maybe always, vague. I'll discuss this in another article.