I suggest the VNM Expected Utility Theorem and this theorem should be used as a test on potential FAI researchers. Is their reaction to these theorems "of course, the FAI has to be designed that way" or "that's a cool piece of math, now let's see if we can't break it somehow"? Maybe you don't need everyone on the research team to instinctively have the latter reaction, but I think you definitely want to make sure at least some do. (I wonder what von Neumann's reaction was to his own theorem...)