Political arithmetic and the state

Sir William Petty (1623-87) was trained as a doctor, became Professor of Anatomy at Oxford and Professor of Music at Gresham College, and was one of the founder members of the Royal Society. His key idea was to apply Baconian scientific method, the use of "number, weight and measure," to social and political issues. This was "political arithmetic," which aimed to provide impersonal, numerical facts as a basis for policy.

His great early achievement, the mapping of Ireland, illustrates his attitude. He had gone to Ireland as physician to Cromwell's army, but he bid for and won the contract to survey the country. His map was an outstanding scientific and organizational achievement - perhaps the best map of any country at the time, finished on time and within budget - but its purpose was to help with the distribution of land to members of the victorious army. Petty himself emerged with extensive lands in Ireland. He was fiercely ambitious, and attached himself to whoever was in power, switching allegiance from Cromwell to Charles II at the Restoration (as, of course, many others did). His policy proposals were designed to strengthen the state, almost regardless of individual rights or interests. To make Ireland more secure and profitable for the British state, for example, he advocated transferring most of the Irish to England, to be absorbed into the much larger English population and eliminated as a separate people with a different language and culture.

The most important of the state's resources is its population, so population estimates were the backbone of political arithmetic. The key work was the

Observations on the Bills of Mortality (1662), by John Graunt (1620-74). Petty certainly collaborated with Graunt and made similar calculations of his own, but their exact roles are unclear. Records of deaths and christenings showed that England as a whole produced a healthy surplus of births over deaths, but that London could only maintain and increase its population by migration from the rest of the country. Petty went on to use estimates of population and assumed per capita income levels to make pioneering estimates of total national income.

What use Petty made of these estimates, and the way they fit into the context of his time, can best be seen in his Political Arithmetick of 1676 (published posthumously in 1690; see Petty, 1899, pp. 233-313). He stated and supported ten conclusions, including:

That a small Country, and few People, may ... be equivalent in Wealth and Strength to a far greater People and Territory That France cannot... be more powerful at Sea than the English or Hollanders That the People and Territories of the King of England are naturally near as considerable, for Wealth and Strength, as those of France That one tenth part, of the whole Expence of the King of England's subjects; is sufficient to maintain one hundred thousand Foot, thirty thousand Horse, and forty thousand Men at Sea, and to defray all other Charges, of the Government That the King of England's Subjects have Stock, competent, and convenient to drive the Trade of the Whole Commercial World. (Petty, 1899, pp. 247-8)

To see this in context, note that Parliament held the purse strings and would not allow Charles II the funds to pursue an active policy. He accepted a subsidy from Louis XIV, effectively making Britain a passive junior partner in French expansionary plans. Petty's calculations showed that England need not be anyone's junior partner. A small country it might be, but it could (and, under a new king, did) aim to control the seas and to dominate the trade of the "commercial world" (essentially the sea-borne trade of Europe). Petty estimated the requirements and the costs with striking accuracy. In the wars around the turn of the eighteenth century, Britain's navy employed just about the 40,000 he proposed. The land army was smaller than his 130,000, but Britain was effectively paying for its allies' troops as well. To do it, taxes had to rise from 3-4 percent of GNP to just about the 10 percent that Petty proposed (Holmes, 1993, p. 439). Petty saw no objection to allowing France to expand on the continent since England's interests lay at sea (Petty, 1927, vol. 1, p. 262), but later generations disagreed.

Petty's writings contain a few digressions that have attracted (perhaps disproportionate) attention. There is a suggestion of a labor theory of value (Petty, 1899, vol. 1, pp. 43, 50-1, 90) and a (conflicting) suggestion that the value of a good might be determined by the labor and land required to produce it, leading Petty to speculate about a "par" or value-conversion factor between labor and land (vol. 1, p. 181). This was later followed up by Cantillon, who referred to Petty's par as "fanciful" (Cantillon, 1755, p. 43). There are also passages that describe some notion of a surplus of output over necessary subsistence (e.g., Petty, 1899, vol. 1, pp. 30, 118). Petty did not follow up any of these in a systematic way and nor did anyone else, at least in Britain (there may be a line of descent via Cantillon and Quesnay in France). To some who think that the labor theory of value and the notion of surplus are particularly important, these digressions seem significant. Seen in the context of the time, however, what is important in Petty is, rather, his emphasis on quantification and on the role of different sectors (agriculture, trade) in the economy as measured by their contribution to income and to tax revenue.

Petty and Graunt had a number of successors. Edmund Halley (the astronomer, 1656-1742) improved on Graunt's population modeling using better data (from Silesia). Gregory King (1648-1712) produced updated estimates of population and national income, which were not published until later but were drawn on by Charles Davenant (1656-1714) in the 1690s. "Political Arithmetic," as defined by Petty, did not survive long beyond the end of the seventeenth century and was harshly criticized in the eighteenth century for excessive reliance on unreliable data.

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