Dealing with the problem of pure staff accumulation, all our researches so far completed point to an average increase of 5.75 per cent per year. This fact established, it now becomes possible to state Parkinson’s Law in mathematical form: In any public administrative department not actually at war, the staff increase may be expected to follow this formula —
x=(2km + l) / n
k is the number of staff seeking promotion through the appointment of subordinates; l 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. x will be the number of new staff required each year. Mathematicians will realize, of course, that to find the percentage increase they must multiply x by 100 and divide by the total of the previous year, thus:
100 (2km + l) / y n %
where y represents the total original staff. This figure will invariably prove to be between 5.17 per cent and 6.56 per cent, irrespective of any variation in the amount of work (if any) to be done.
The discovery of this formula and of the general principles upon which it is based has, of course, no political value. No attempt has been made to inquire whether departments ought to grow in size. Those who hold that this growth is essential to gain full employment are fully entitled to their opinion. Those who doubt the stability of an economy based upon reading each other’s minutes are equally entitled to theirs. It would probably be premature to attempt at this stage any inquiry into the quantitative ratio that should exist between the administrators and the administered. Granted, however, that a maximum ratio exists, it should soon be possible to ascertain by formula how many years will elapse before that ratio, in any given community, will be reached. The forecasting of such a result will again have no political value. Nor can it be sufficiently emphasized that Parkinson’s Law is a purely scientific discovery, inapplicable except in theory to the politics of the day. It is not the business of the botanist to eradicate the weeds. Enough for him if he can tell us just how fast they grow.
C. Northcote Parkinson, “Parkinson’s Law, or the rising pyramid”, Parkinson’s Law (and other studies in administration), 1957.
June 13, 2014
QotD: Mathematical formula describing bureaucratic growth
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