Can a single case be used to test theory? 

 Every so often, I try to take some time to read something that I should have read ages ago.  Tonight's gem was the 2010 draft of "The Industrial Organization of Rebellion: The Logic of Forced Labor and Child Soldiering" by Bernd Beber and Chris Blattman ( link ).  The paper gets a lot of traction out of a formal model and then matches these predictions up to reality using some unique and hard-earned data.   

 An off-hand comment in the paper caught my attention: Beber and Blattman's assertion that  "a single case helps to refine our theory and validate some basic assumptions, but cannot test it"  (p 19).  Ordinarily I'd say "sure", except that they are referring to their own nuanced analysis of a large number of child soldiers painstakingly tracked down in Uganda.  Moreover, they actually have a credible identification strategy -- abduction into the Lord's Resistance Army was essentially random after conditioning on age and location.  I was pretty convinced by the analysis; more so than by the regressions on the novel but dubious rebel dataset they introduce at the end of the paper.  Maybe the Uganda child-soldier analysis wasn't a "test" but it sure moved my posterior beliefs about their hypotheses. 


 So, I wonder what they meant.  I guess I can just email them and ask, but that would be no fun.  Instead, I'll speculate wildly.   

 One possibility is that the Uganda data was collected and analyzed prior to the development of the model.  Or perhaps they are noting that there isn't any variation in rebel groups, so we obviously can't estimate the effect of some of their important moving parts (motivating the turn to other data).  On the other hand, their theory does generate a number of observable implications that they do successfully  test  "validate" with the child-soldiering data.  And like I said, it was this evidence that convinced me.  I think even the realize this: they spend 8 pages on Uganda and 4 on the cross-rebel group comparisons. 

 I think the usefulness of single cases is worth pondering, especially since it's often much easier to get the kind of unique data that allows causal identification for a single case!