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January 20, 2009
The Mathematics of Bureaucracy
Three physicists and a historian explain how bureaucracies grow and at what point they become inefficient. They define how big a committee can become before destabilizing.
In 1947, German sociologist Max Weber published The Theory of Social and Economic Organisation, which outlined his theory on management. He proposed three types of organizational leadership: charismatic, hereditary and bureaucratic. Of the three, bureaucratic was explained to be the most efficient.
Weber theorized that in the bureaucratic stage, "everything runs with machine-like efficiency, and authority and control are exercised 'on the basis of knowledge,'" according to The Economist. The organization follows a specified division of labor (which Weber argues needs to be formally recorded) and a linear structure for promotion based on the judgment of superiors within a formal hierarchy.
A 2004 paper, titled Using the Lens of Max Weber's Theory of Bureaucracy to Examine E-Government Research, also notes that Weber believed bureaucracy to be ideal for administration because its "institutionalized rules and regulations enabled all employees to learn to perform their duties optimally."
Although he saw many advantages for this arrangement, Weber also believed that in practice, it could become an "iron cage" for employees who are bogged down with excessive controls. He also lamented that bureaucracies will become an end in and of itself and will ultimately cease serving society, the IEEE Computer Society paper states.
Weber's criticism of bureaucracy is probably closer to how many people see it today. John Pourdehnad, management consultant and educator, agrees with Weber's criticism, writing on his blog that a bureaucracy "takes steps to preserve itself: It makes work and introduces red tape, and it imposes nonfunctional requirements on others, which 'justify' the made work."
Pourdehnad also adds that because people are being promoted based on seniority rather than merit, the bureaucratic organization continues to grow uncontrollably. "Since performance is not critical for survival, size is. ...Therefore, growth becomes an objective because it is an efficient way to secure survival," he argues.
Parkinson's Law, theorized by C. Northcote Parkinson, a British Royal Navy historian and author, explains this phenomenon by stating that "work expands to fill the time available for its completion" and in bureaucratic organizations, the number of people required to do the work will continually rise whether the actual volume of work stays the same, increases, decreases or disappears. (Source: New Scientist)
According to Parkinson, this occurs because workers want to multiply subordinates, not rivals, and make work for each other. For example, an overworked employee wants to diminish the amount of work he has to do. He can either: 1) resign, 2) halve the work with a colleague of equal standing in the company or 3) hire two junior employees to work under him.
The first option leaves him jobless, and the second brings a potential rival for a promotion. The third option is the only one that allows him to keep his standing in the company while allowing him to do less. It is also important to note that he requires two subordinates, because if only one were hired, he'd potentially end up with a rival again.
Inevitably, says Parkinson, the two subordinates will feel overworked and will want to hire people (two for each) to work below them. Now the organization has seven people doing the work that one person used to do not exactly the model of efficiency Weber hoped for. In mathematical form, Parkinson's Law follows the formula:
Here, "k" is the number of staff seeking promotion through the appointment of subordinates; "p" represents the difference between the ages of appointment and retirement; "m" is the number of man hours devoted to answering minutes within the department; and "n" is the number of effective units being administered. Then "x" will be the number of new staff required each year.
To find the percentage increase, multiply "x" by 100 and divide by the total of the previous year. The percentage will "invariably prove to be between 5.17 percent and 6.56 percent."
So how can organizations avoid this uncontrolled growth and inefficiency, both in the organization as a whole and within its decision-making committees?
Based on Parkinson's Law, physicists Peter Klimek, Rudolf Hanel and Stefan Thurner of the Medical University of Vienna in Austria came up with a model under which conditions bureaucratic growth can be confined. The three assigned efficiency curves to workers throughout their life and computed the time when they should optimally retire, or what Parkinson referred to as the "Pension Point," to ensure a "maximum efficiency within the body."
The physicists also came up with a way to quantify how large a committee can grow before it becomes inefficient. The number they came up with is 20 (see graph, right). As explained to New Scientist, their simulation grouped committee members into "tightly knit clusters with few further links between clusters tying the overall network together." This setup is intended to reflect the clumping tendencies of like-minded people in human interactions.
Each person in the committee had one of two opposing opinions. At each step in the model, each member would adopt the opinion held by a majority of their immediate neighbors within the cluster and then between clusters. The simulations resulted in a consensus or got stuck at an entrenched disagreement between two factions.
They found that groups with fewer than 20 members tend to reach an agreement whereas those with more than 20 splintered into groups that agreed within themselves but remained deadlocked as a whole. Additionally, the computer simulations found one number of members that ended with a high probability of deadlock: eight. (It is perhaps worth noting that 90 percent of small businesses in the U.S. employ fewer than 20 people, according to the National Federation of Independent Business.)
In 1955, Parkinson noted that no nation had a cabinet of eight. As New Scientist points out, only one British monarch in U.K. history had eight council members: Charles I. His and his cabinet's decision-making led to the English Civil War and eventually his beheading.
Resources
Classical Organization Theory: Bureaucracy, Power and Control
HRM Guide (U.K. Human Resources)
Max Weber
The Economist, Jan. 9, 2009
Using the Lens of Max Weber's Theory of Bureaucracy to Examine E-Government Research
by Aby Jain
System Sciences (IEEE Computer Society), 2004
Bureaucracy as a Mechanism to Generate Information
by Walter Novaes and Luigi Zingales
RAND Journal of Economics / Entrepreneur Magazine, summer 2004
In Bureaucracy, Size Matters!
by John Pourdehnad
Negotiating Bureaucracy (BusinessWeek), July 1, 2008
Parkinson's Law
by C. Northcote Parkinson
The Economist, November 1955
C. Northcote Parkinson and His Theory of Bureaucratic Growth
by Julie Novak
The Political Economist, Nov. 17, 2008
Explaining the Curse of Work
by Mark Buchanan
New Scientist, Jan. 14, 2009
Parkinson's Law Quantified: Three Investigations on Bureaucratic Inefficiency
by Peter Klimek, Rudolf Hanel and Stefan Thurner
Cornell University Library, Aug. 12, 2008
Quantifying Inefficiency
by Anders Sandberg
Andart blog, Aug. 22, 2008
Small Business Facts
National Federation of Independent Business
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Comment
2 CommentsThe above referenced paper appears to be fairly simplistic. Even with the simplifications, there are better (and much more complex methods) in which to attack this difficult problem. It is a highly nonlinear system that needs to be analyzed in the ways that nonlinear systems are analyzed by experienced engineers.
January 20, 2009 6:27 PMThis is one great article. I might want to reproduce copies some time. Who do I contact?
February 25, 2009 4:53 PM


