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Coefficient of Inefficiency is a semi-humorous attempt of C. Northcote Parkinson to define the size of a committee or other decision making body at which it becomes completely inefficient.
In the book Parkinson's Law: The Pursuit of Progress, (London, John Murray, 1958) one of the chapters is devoted to the basic question of comitology: how committees, (government) cabinets and other such bodies are created, grow to be eventually of no relevance, or are designed such from the beginning.
Empirical evidence is drawn from government cabinets from history and contemporary evidence. Most often the minimal size of a state's most powerful and prestigious body is five members. From English history, Parkinson notes that the first cabinet has been the Council of the Crown, now the House of Lords, which has grown from an unknown initial number to 29 to 50 before 1600, when it has also lost much of its power. A new body was appointed in 1257, the "Lords of the King's Council" numbering less than 10. The body grew and eventually ceased to meet when it numbered 172 members. The third incarnation of the English cabinet was the Privy Council, initially also numbering less than 10 members. Inversely with rising membership (47 in the year 1679) the Privy Council lost power to the new (fourth incarnation) Cabinet Council, in 1615. Numbering initially eight members, it grew to 20 by 1725. In about 1740 the Cabinet Council was superseded by an inner group, called the Cabinet, numbering five in the beginning. At the time of Parkinson's study (the 1950s) this was still the official governing body. Parkinson's observation is that from 1939 on there was an effort to save the Cabinet as an institution. The membership has been fluctuating from a high of 23 members in 1939, down to 18 in 1954.
A fancy mathematical expression is proposed by Parkinson for the Coefficient of Inefficiency, featuring many possible influences. The formula remains to be empirically confirmed. Parkinson's conjecture that membership exceeding a number "between 19.9 and 22.4" makes a committee manifestly inefficient seems well justified by the evidence proposed. Less certain is the optimal number of members, which must lie between three (a physical minimum) and 20. That it may be eight seems both justified and ruled out by observation: no contemporary government in Parkinson's data set had eight members, and only the unfortunate king Charles I of England had a Committee of State with that membership.
- Parkinson's Law, or The Pursuit of Progress, C. Northcote Parkinson, 1957. 
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