Published online 22 August 2008 | Nature | doi:10.1038/news.2008.1050

Column: Muse

Battling bureaucracy with maths

In committees, work expands to fill the time available while growth brings inefficiency. It's worth trying to figure out why, says Philip Ball.

The European Union (EU) is notoriously bureaucratic. The reason, most observers agree, is that there are too many member states pulling in different directions to actually achieve anything. But how many members is too many?

Committee meetingNow take away the number you first thought of...Punchstock

A group of scientists now claims to have the answer. The researchers have developed a mathematical model that shows that decision-making bodies start to suffer from inefficiency once they grow beyond about 20 members.

The EU exceeds that by seven members. Indeed, the Treaty of Lisbon, which proposes various reforms in an attempt to streamline the EU's workings, implicitly recognizes the overcrowding problem by proposing a reduction in the number of European Commissioners to 18. As if to prove the point, Ireland rejected it in June.

It's not hard to pinpoint the problem with large committees: the bigger the group, the harder it is to reach a consensus. This has doubtless been recognized since time immemorial, but it was stated explicitly in the 1950s by the British historian C. Northcote Parkinson. He pointed out that British governing councils and cabinets since 1257 seemed to go through a natural life cycle: they grew until they far exceeded a 'coefficient of inefficiency' of about 20 members, and were then replaced by a new body that eventually suffered the same fate.

Critical mass

Stefan Thurner and his colleagues at the Medical University of Vienna, Austria, have attempted to put Parkinson's anecdotal observations on a solid theoretical footing. Cabinets are now a feature of governments worldwide, and the researchers found that most of those from 197 self-governing countries have between 13 and 20 members. What's more, the bigger the cabinet, the less well it seems to govern the country, as measured by the Human Development Indicator, an index used by the United Nations Development Programme that takes into account such factors as life expectancy, literacy and gross domestic product.

Thurner and his colleagues have tried to understand where this critical mass of 20 comes from by using a mathematical model of decision-making in small groups1. They assume that each member may influence the decisions of a certain number of others. Each adopts the majority opinion of those to whom he or she is connected, provided that this majority exceeds a certain threshold.

For a range of model parameters, a consensus is always possible for less than 10 members — with the curious exception of 8. For committees with more than 10 members, consensus becomes progressively harder to achieve. When it reaches 19-21 members the number of ways the committee can fail to reach consensus increases significantly, in line with Parkinson's observations.

The problem with eight-member groups appears to be a mere numerical quirk of the model chosen, but it's interesting that no eightfold cabinets appeared in the authors' global survey. Historically, only one such cabinet seems to have been identified: the Committee of State of the British king Charles I, whose Parliament rebelled and eventually executed him.

Just enough work to fill the time

The Austrian researchers then extended their analysis of Parkinson's ideas to the one for which he is best known: Parkinson's Law, which states that work expands to fill the time available2. This law provided the title of the 1957 book in which Parkinson's essays on governance and efficiency were collected.

Parkinson regarded his law as a corollary of the inevitable expansion of bureaucracies. Drawing on his experience as a British civil servant, he pointed out that officials aim to expand their own mini-empires by gathering a cohort of subordinates. But these people simply make work for each other, dwelling over minutiae that would otherwise be ignored.

Parkinson's analysis of this effect focused on the issue of promotion, which is in effect what happens to someone who acquires subordinates. His solution was to engineer a suitable retirement strategy so that promotion remains feasible for all.

With promotion, he suggested, individuals progress from responsibility to distinction, dignity and wisdom. Without it, the progression is instead from frustration to jealousy to resignation and oblivion, with an associated decrease in efficiency. This has become known as the 'Prince Charles Syndrome', after the British monarch-in-waiting who seems increasingly desperate to find a meaningful role in public life.

Natural laws

The researchers have couched these ideas in mathematical terms by modelling organizations as a flow of staff. They find that as long as promotion prospects can be sufficiently maintained, exponential growth can be avoided. The key is to adjust the retirement age according to the size and structure of the organization, to maximize the efficiency of it members.

Of course, precise numbers in this sort of modelling should probably be taken with a pinch of salt. Yet correlations like those spotted by Parkinson, and now fleshed out by Thurner and his colleagues, do seem to be telling us that there are natural laws of social organization that we ignore at our peril.

The secretary-general of the North Atlantic Treaty Organisation (NATO) has just made positive noises about Georgia's wish for membership, for example. This may or may not be politically expedient in the current climate; but with NATO membership currently at a bloated 26, he ought at least recognize what the consequences might be for the organization's ability to function. 

  • References

    1. Klimek, P., Hanel, R. & Thurner, S. Preprint at http://arxiv.org/abs/0804.2202 (2008).
    2. Klimek, P., Hanel, R. & Thurner, S. Preprint http://arxiv.org/abs/0808.1684 (2008).
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