Formal Models of Bureaucracy

Formal analysis is fairly new in public administration, and there is some scepticism in the field about the intellectual advantages of mathematical methods. This is appropriate. Using these methods is now faddish, and fads can cause goal displacement. A formal model of bureaucracy should be only a tool for deepening our knowledge about public organizations. If the underlying ideas are silly, translating them into mathematics will do little good. If they are promising, however, deductive reasoning can help us explore their potential: if one believes A is a general property of bureaucracies, to fail to work out A's logical implications would be throwing away information. Analysis can also increase the falsifiability of our ideas: if A implies B but empirically we find not-B, the truth status of A is brought into question. Or it may turn out, as Arrow discovered about democratic principles, that our informal ideas are logically inconsistent: we thought properties C and D describe existing or possible institutions, but recasting the ideas into mathematical form reveals that such an institution is impossible. Finally, some problems are just too hard to tackle without formal tools. It is unlikely, for example, that Robert Axelrod would have discovered the robustness of the simple strategy of tit-for-tat in the two person prisoners' dilemma without the help of a computer (to pit tit-for-tat against many opponents in thousands of rounds of play) and of mathematics (to prove some generic properties of tit-for-tat).