CONTINUOUS APPROXIMATIONS IN THE STUDY OF HIERARCHIES

Large organizations are typically modelled as hierarchies. Hierarchies are discrete structures (trees), but researchers frequently use conti nuous approximations. The purpose of this article is to study the vali dity of these approximations. I show that modelling hierarchies with a continuum of tiers is not a good approximation. I also show, for a pa rticular model of balanced hierarchies, that ignoring rounding operato rs and integer constraints in formulae derived from the discrete model can be a valid approximation, when hierarchies are suitably large. Th is is made precise by bounds on the relative errors of the approximati ons.