Pareto: the Pareto "law" and the receipts

Vilfredo Pareto has never been a well known name, outside of economics and a part of sociology. He has, however, entered popular culture due to his so called “80/20” law, a power law that is often used by conservatives to indicate that inequality is not caused by social arrangements but transcends them – is rooted, in fact, in human nature.

In many ways, Pareto, who lived during a time when the classical liberal order was dissolving, prefigured neoliberalism. He advocated for two theses that have become part of neo-liberal doctrine. The first is that inequality isn’t bad, poverty is: thus, growth is the way out of poverty, and the only real economic concern of the state. The other thesis, which he called the “circulation of elites”, is that family wealth – wealth attached, as it were, to the house – does not secure a specific elite over time. In other words, social mobility is such that the rich become poor and some of the poor become rich.

These two theses make up the apologetic for capitalism in our time. It is for this reason that taking a critical view of Pareto is a politically charged act.

It is one of the peculiarities of the secondary literature on Pareto that so few are interested in the sources from which he took his statistics to derive his  famous “law” of the distribution of income. Admittedly, Pareto himself simply articulated a power law in which the significant variable {a} could be a bit different. Still, he was very sure that he had stumbled upon a statistical relation that must, somehow, be rooted in human nature, and he claimed that he did so empirically: by looking at statistics about total income and its distribution in various countries. In other words, Pareto didn’t bring his power law to these stats, they brought the power law to him. Pareto used that law to attack socialistic schemes for equality. Go to twitter and advocate for equality, and [by a special power law I will entitle Gathmann’s law] before the string of replies is complete, someone will have invoked the 80/20 law, or some distorted form of it. It has become business school wisdom, which is where all truisms go to be shined up for perky MBAs to pour forth to the workers.

According to Jean-Sebastian L’enfant’s study of the Pareto law, Pareto viewed statistics from colonial Peru as an affirmation of what he had (supposedly) found in studying income distribution in Europe – his 80/20 law.

“Ainsi, lorsqu’il constate que sa loi peut tout aussi bien décrire la répartition des revenus au Pérou, à la fin du XVIIIème siècle 14, il n’hésite pas à y voir une confirmation et un motif de généralisation : “une coïncidence fortuite est possible mais peu probable, et il se pourrait qu’une même cause eût produit les mêmes effets observés” (Pareto, 1897a, 46). C’est en tout cas un indice supplémentaire que la distribution des revenus n’obéit décidément pas au hazard. [Thus, when he observed that his law could describe, as well, the distribution of incomes at the end of the 18^th century, he didn’t hesitate to see in this a confirmation and a motive to generalization: “a fortuitous coincidence is possible but not very probable, and it could be that the same cause produces the same observed effects.” In any case this was a supplementary index that the distribution of incomes did not obey mere chance.

This statement interested me. Knowing that statistics for colonial Peru, especially as they were available to a historian who was writing in the late eighteenth century in Britain, were unlikely to be extensive, I went to Pareto’s text. Pareto writes:

Curious information is furnished to us by W. Robertson on Peru, at the time of Spanish rule, at the end of the 18^th century. They sold there a certain [papal] bull, said to be from the crusades, and everyone bought it, Spaniard creole or mulatto, at a price fixed by the government.. the price of the bull varied according to the rank of persons.”

Robertson gives us the numbers of persons who bought the bull. We find here, approximately, the law that we saw presiding over the distribution of total income.”

Pareto then constructs a little table of figures derived from Robertson. It is all very neat. Yet when we look at what Robinson says, huge gaps appear in this account. It should be said Robertson uses the figures on the issuances of the bull to make an estimate at the population of Peru, since he has no census figure, (evidently he was not  familiar with the Peruvian census of 1740 – which he would not have had access to anyway in the 1790s). Even so, these figures themselves are shaky. In Robertson’s account, from whence Pareto derives his numbers, the reference source is not quoted, and Robertson falls back on numbers of copies of the bulls printed, not bought.  And one thing Robertson tells us straight out: the figures tell us nothing about the Indian population, since so few Indians bought the bull from the government,  even though he estimates that the Indians were perhaps the majority of the population. Other sources – not Robertson – have implied that there was a strong secondary market in the bula – it was, basically, a bull of indulgence. Thus, Indians may not have bought it from the government, but they did from salesmen who bought it from the government. So we are talking about a product that was bought both for consumption and for sale – which already tells us that we cannot use these figures as a proxy for income distribution, any more than we could use figures about television sets that mix up wholesale and retail sales. Robertson never gives his source for the sales of the bull, although he claims that he believes they are accurate. He gives an estimate for the Indian population as around 2,600,000 from another source before he gets to the bulls.

 “According to an account which I have reason to consider as accurate, the number of copies of the bull of cruzada exported to Peru on each new publication, is 1,171,953; to New Spain, 2,649,326. I am informed that but few Indians purchase bulls, and that they are sold chiefly to the Spanish inhabitants, and those of mixed race.”

Comparing Pareto’s source to what Pareto claims Robertson says, we do have to say that chance plays probably plays little role in the emergence of Pareto’s power law, here. What seems to play the biggest role is Pareto’s own obsession. The printing of these bulls, at different prices, from an indeterminate source, over a period of at least two hundred years, does not offer empirical confirmation except through the most hazardous of conjectures. We have Robertson’s numbers, at best, for the “last predication”, which is undated, although the selling of these bulls goes back to the sixteenth century. So what we have is the essence of an unsound method for making statistical analysis. Far from being an independent confirmation of the Pareto law, the Robertson quote seems to be a confirmation of a hermeneutic tendency: to assume the law and look for instantiations.

Yet I have yet to read any doubt about Pareto’s method for gathering his data. And perhaps his data set  from Italy is sound. Pareto’s leaping upon confirmation in his reading of a hundred year old text about Peru, in spite of its own author’s cautions, gives me pause, though.