Mark Buchanan writes in issue 2690 of New Scientist magazine, page 38-39:
Is there anything more to that "law" than just a cynical slogan? Physicists Peter Klimek, Rudolf Hanel and Stefan Thurner of the Medical University of Vienna in Austria think so. They have recreated mathematically just the kind of bureaucratic dynamics that Parkinson described anecdotally 50 years ago. Their findings put Parkinson's observations on a scientific footing, but also make productive reading for anyone in charge of organising... well, anything.
Parkinson based his ideas not just on his war experience, but also his historical research. Between 1914 and 1928, he noted, the number of administrators in the British Admiralty increased by almost 80 per cent, while the number of sailors they had to administer fell by a third, and the number of ships by two-thirds. Parkinson suggested a reason: in any hierarchical management structure, people in positions of authority need subordinates, and those extra bodies have to be occupied- regardless of how much there actually is to do.
Parkinson was crystallising, with tongue half in cheek, classic work done by the German sociologist Max Weber in the early 20th century. Weber described the attributes of an ideal bureaucracy and possible "degenerating" influences - such as any system of promotion not based wholly on merit. Parkinson's own analysis spawned other, more po-faced and politically charged critiques of public bureaucracies from economists such as William Niskanen, who served on US President Ronald Reagan's Council of Economic Advisers. Niskanen theorised that bureaucracies grow because officials seek to increase the budgets they control and so boost their own salary, power and standing. He and other conservatives used such arguments to push for smaller government - but they could not give any supporting quantitative insight into the growth of bureaucracies.
The new work aims to do just that. "Parkinson's essays weren't quantitative," says Klimek, "but they're so clear that it's easy to cast them into specific mathematical models." From a simple system of equations using quantities such as the promotion and drop-out rates within a hierarchical body, a "phase diagram" can be computed to show what conditions breed ever greater bureaucracy. A high probability of promotion coupled with the hiring of more subordinates - the scenario Parkinson described- is unsurprisingly a recipe for particularly fast growth.