IT IS 1944, and there is a war on. In a joint army and air force headquarters somewhere in England, Major Parkinson must oil the administrative wheels of the fight against Nazi Germany. The stream of vital paperwork from on high is more like a flood, perpetually threatening to engulf him.
Then disaster strikes. The chief of the base, the air vice-marshal, goes on leave. His deputy, an army colonel, falls sick. The colonel's deputy, an air force wing commander, is called away on urgent business. Major Parkinson is left to soldier on alone.
At that point, an odd thing happens - nothing at all. The paper flood ceases; the war goes on regardless. As Major Parkinson later mused: "There had never been anything to do. We'd just been making work for each other."
That feeling might be familiar to many working in large organizations, where decisions can seem to be bounced between layers of management in a whirl of consultation, circulation, deliberation and delegation. It led Major Parkinson - in civilian dress, C. Northcote Parkinson, naval historian, theorist of bureaucracy and humorist- to a seminal insight. This is "Parkinson's law", first published in an article of 1955, which states: work expands to fill the time available for its completion.
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.
Parkinson was also interested in other aspects of management dynamics, in particular the workings of committees. How many members can a committee have and still be effective? Parkinson's own guess was based on the 700-year history of England's highest council of state- in its modern incarnation, the UK cabinet. Five times in succession between 1257 and 1955, this council grew from small beginnings to a membership of just over 20. Each time it reached that point, it was replaced by a new, smaller body, which began growing again. This was no coincidence, Parkinson argued: beyond about 20 members, groups become structurally unable to come to consensus.
A look around the globe today, courtesy of data collected by the US Central Intelligence Agency, indicates that Parkinson might have been onto something. The highest executive bodies of most countries have between 13 and 20 members. "Cabinets are commonly constituted with memberships close to Parkinson's limit," says Thurner, "but not above it." And that is not all, says Klimek: the size of the executive is also inversely correlated to measures of life expectancy, adult literacy, economic purchasing power and political stability. "The more members there are, the more likely a country is to be less stable politically, and less developed," he says.
Why should this be? To find out, the researchers constructed a simple network model of a committee. They grouped the nodes of the network - the committee members- in tightly knit clusters with a few further links between clusters tying the overall network together, reflecting the clumping tendencies of like-minded people known to exist in human interactions. To start off, each person in the network had one of two opposing opinions, represented as a 0 or a 1. At each time step in the model, each member would adopt the opinion held by the majority of their immediate neighbours.
Such a process can have two outcomes: either the network will reach a consensus, with 0s or 1s throughout, or it will get stuck at an entrenched disagreement between two factions. A striking transition between these two possibilities emerged as the number of participants grew - around Parkinson's magic number of 20. Groups with fewer than 20 members tend to reach agreement, whereas those larger than 20 generally splinter into subgroups that agree within themselves, but become frozen in permanent disagreement with each other. "With larger groups, there's a combinatorial explosion in the number of ways to form factions," says Thurner.
Santo Fortunato, a physicist who works on complex networks at the Institute for Scientific Interchange in Turin, Italy, thinks the result is convincing evidence for Parkinson's conjecture. But he would like to see further testing. "The outcome might well change significantly if you change the shape of the social network, or the way people's opinions influence one another," he says.
So might this kind of work offer a rational way to optimise our decision-making bodies? One curious detail provides an intriguing slant on this question. In the computer simulations, there is a particular number of decision-makers that stands out from the trend as being truly, spectacularly bad, tending with alarmingly high probability to lead to deadlock: eight.
Where this effect comes from is unclear. But once again, Parkinson had anticipated it, noting in 1955 that no nation had a cabinet of eight members. Intriguingly, the same is true today, and other committees charged with making momentous decisions tend to fall either side of the bedevilled number: the Bank of England's monetary policy committee, for example, has nine; the US National Security Council has six.
So perhaps we all subliminally know the kind of things that Parkinson highlighted and the computer simulations have confirmed. As Parkinson noted, we ignore them at our peril. Charles I was the only British monarch who favoured a council of state of eight members. His decision-making was so notoriously bad that he lost his head.
- Parkinson's Law, or The Pursuit of Progress by C. Northcote Parkinson (Murray, 1958)