How Heterogeneity Shapes Vilfredo Pareto s Social Equilibrium

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1 How Heterogeneity Shapes Vilfredo Pareto s Social Equilibrium Gianfranco Tusset* Abstract: The current idea of the representative agent cannot be readily applied to Vilfredo Pareto s analysis, which is predicated on the heterogeneity of individuals. Indeed, recognition of the importance of heterogeneity leads Pareto to introduce statistical equilibrium as a complement to the theoretical equilibrium that results from a balance of economic forces. The purpose of this paper is to highlight the implications of Pareto s views on heterogeneity for the study of political economy and to draw attention to the largely Italian literature that stresses Pareto s anticipation of aspects of statistical equilibrium developed in the physical sciences. 1 Introduction The work of Vilfredo Pareto on economics, sociology and political sciences has been the subject of interest in each of these disciplines for its well-known innovative results. But further interesting insights can be obtained by considering features that recur commonly across his extensive scientific contributions to each of these three disciplines. One such feature is the heterogeneity of social and economic agents, 1 whose meaning can be inferred from the following quotation: We can define society as a heterogeneous and hierarchical aggregate. Human beings differ in sex, age, moral, intellectual and physical qualities, etc. (1905: 298). This statement testifies that Pareto, as a follower of Machiavelli, 2 considered the heterogeneity of individuals as a natural fact, where natural means that differences among individuals are common to all societies regardless of time and place: natural did not imply harmony or spontaneous order, but it may be understood as in an individual struggle. 3 This natural or individual conception of heterogeneity is perfectly consistent with Pareto s supposed methodological individualism, although it raises questions in regard to the requirement of aggregating heterogeneous individuals. Pareto provided an answer, although not a fully developed one: the analysis of many different individuals within a social system requires statistical equilibrium that reflects an analogy with physics. Statistical equilibrium, as established in the kinetic theory of gases, proved an appropriate tool when considering the effect of oscillating movements of different elements within a system that largely offset each other in the aggregate, with global equilibrium, or stable trend, often revealed. In regard to social phenomena, however, Pareto regarded heterogeneous individuals as culturally biased and dominated by sentiments, which he suggested lead individuals to aggregate, like molecules, into groups of individuals who share similar interests or sentiments, with the broad social aggregate comprising many such groups. The aim of the paper is to delve into the relation between the assumption of heterogeneity and the introduction of a statistical notion of equilibrium that complements the general equilibrium of pure economic theory that is determined by the balance of economic forces. Although the individual elements of society may appear irregular, even chaotic, the level of disorder may be reduced when individuals are aggregated into sub-groups according to their culture and sentiments History of Economics Review No. 57 (Winter)

2 48 History of Economics Review with a view to identifying a statistical equilibrium. From that perspective, heterogeneity itself becomes as a source of equilibrium and order because it induces individuals to organise themselves into groups that generate social dynamism. Pareto, in this theory of social equilibrium, classed heterogeneity as one of the four categories that enliven a society, together with residues, 4 (economic) interests and derivations 5 (Pareto 1916: sec. 2205), made it clear that differences among groups favour the circulation of élites and, as we shall see, make the entire economy more dynamic. It is precisely the dynamism of a society that provides for the possibility of stability in the social equilibrium. Thus, whilst the idea of statistical equilibrium applied to economics leads to a conception of society as a heterogeneous set, the dynamic relationships among these different agents and aggregates are necessary for social equilibrium and stability. According to this view, the notion of equilibrium applied by Pareto to society in his last works assumes new interesting meanings for the study of economic action. The contribution of this paper is that it points to the importance of social equilibrium, and the underlying dynamic relationships between heterogeneous agents, to the study of political economy. To achieve that goal, Pareto s writings on heterogeneity and social equilibrium as reviewed, and the secondary literature from the 1930s and 1940s on the use of statistical tools in Pareto s social and economic equilibrium, is highlighted. Particular attention is given to Vinci (1924), De Pietri Tonelli (1931), Palomba (1935), Bernardelli (1943), D Addario (1949), Davis (1949) and Jannaccone (1949). The sporadic revival of that issue, most notably by Mandelbrot (1963), D Amato (1973) and Morishima (1994), is also considered. Section 2 of this paper presents Pareto s conceptions of heterogeneity throughout his work. Section 3 investigates Pareto s statistical conception of equilibrium. Section 4 highlights the role of aggregates and social dynamism in determining social equilibrium. Section 5 sketches some development of Pareto s insights on statistical equilibrium. Section 6 makes some brief concluding remarks. 2 Heterogeneity throughout Pareto s Work Pareto conceived heterogeneity as an observed feature of societies. Indeed, he regarded it as such a clear basic social trait that it represents a starting point for economic and social theorisation. Whilst observed data concern individual or natural heterogeneity involving relationships among groups, social heterogeneity may require abstraction or theorisation which adds conjectures to observed facts. Thus the analysis could be either more empirical or more theoretical according to the specificity of the context. Pareto stated in the Cours ( : sec. 574) that observation is the simple description of phenomena and their laws, whereas empirical or rational laws must be deduced and not only observed. Indeed, simple data are the outcomes of observation (Pareto : sec. 629); then interpolation and other forms of data treatment make it possible to draw curves representing laws. Pareto ( : sec. 629, n. 1) wrote that: The distinguishing character of experimental sciences consists of making use of premises drawn from experience. He repeatedly stated that observing is experimenting. But experimentation was gradually set aside and the word was used in the sense of observation. In the Manual he wrote: When we speak of the experimental method, we are expressing ourselves in the elliptical manner and we mean the method, which makes use either of experiment or of

3 Pareto s Social Equilibrium 49 observation, or of two together if that is possible (1906: 12). Certainly, observation precedes theorisation, as Pareto specified: it might perhaps be better to say observation and reasoning instead of reasoning and observation (Pareto 1916: sec. 1537, note 1). Therefore, Pareto s first step is to present heterogeneity as an observed fact: when the latter concerns individuals, including the economic behaviours of individuals, we may say that it results from repeated observations; it is not explained by a theory. Pareto addressed heterogeneity in his early writings. The first observed phenomenon involving heterogeneity was the distribution of income, from which derived the so-called Pareto s law or Pareto s curve. Pareto showed, first in the 1896 articles and then in the Cours, that the upper tail of this distribution comprises the same percentage of the population in different countries and at different times. 6 This corroborated the natural character of heterogeneity: that is, it should not be related to time and space. 7 Heterogeneity matters here because incomes were naturally distributed in unequal manner, without there being any rational explanation for this disparity. In a sense, this was the first case of uniformity without theory; as Pareto himself maintained, it is an empirical law simple enough (1895: 60). Renato Cirillo wrote that this curve indicates that some sort of order might exist (Cirillo 1974: 276). According to Pareto, this unequal order can be a natural one only, without any historical features. Proof of this is provided by Pareto s attempt to demonstrate that income distribution is not the outcome of causal factors that give rise to a causal explanation of such a distribution. Pareto reversed the causal relation between heterogeneity and inequalities in economic distribution: that is, income distribution does not occur according to some economic process alone, but is also a product of heterogeneity of individuals who present different qualities or capacities. 8 Proposing heterogeneity as a natural fact allows Pareto to argue for a concept of naturalness which differs from the supposed analogous notion of harmony put forward by Smith. Here natural evokes more conflict than harmony or equilibrium. In some sense, the inequality which generates conflicts is intrinsic to modern economies as the result of heterogeneous individuals. In Pareto, any representative agent is replaced by an observed specific agent. The individuals grouped into a certain number of heterogeneous groups (on the basis of income) can be depicted in accordance with a hyperbolic distribution of individual qualities or capacities. The latter causes an analogous distribution of income, with the statistical equilibrium represented by the Pareto distribution of income showing the stable relationship for the aggregate, but concealing the dynamic changes associated with heterogeneous individuals: The outward form [of the curve of income distribution] varies little, the interior portion is, on the other hand, in constant movement; while certain individuals are rising to higher levels, others are sinking (Pareto 1906: 286). Inequality is the first important natural condition generating the differences in the distribution of income. We may then argue about the origins of the unequal distribution of individual qualities, but in the end the naturalness of inequality proves to be a necessary feature. But what are heterogeneous qualities or capacities characterising the individual? How can we measure them? As said, income distribution is an observed fact without any theory explaining it. Felice Vinci (1924: 129), an economist contemporary to Pareto, wrote that the distribution of incomes is a random phenomenon determined

4 50 History of Economics Review by the distribution of qualities and obstacles. Since a country s economic conditions do not matter, Giorgio Mortara (1924: 125), an economist-statistician, stated that only human nature could plausibly explain differences in income distribution. 9 By contrast, Pareto (1906: 284) wrote that the income distribution which he drew is not the curve of the qualities of men, but the curve of other facts related to these qualities. But he did not go beyond reference to exogenous events conditioning income distribution. It seems that the distribution of qualities, and consequently of income, are due to chance; they have no logical explanation. In the Manual, heterogeneity is reaffirmed as a natural phenomenon not requiring causal explanation either and involving social consequences: To these inequalities of human beings per se correspond economic and social inequalities, which we observe among all peoples, from the most ancient times to the present, everywhere in the world, and such that this characteristic is always present. (Pareto 1906: 281) In those years, the idea of applying heterogeneity to aggregates made its appearance. In his Les Systèmes Socialistes, Pareto ( : 80) stated that the features of aggregates are not the sum of those of parties, nor can they be obtained from their juxtaposition the outcome of many things is not the sum of them. This idea is proposed again in the Programme et sommaire du Cours de sociologie: Society is an aggregate different from the individuals forming it, but this does not mean that society can exist independently from those individuals (Pareto 1905: 296). Although Pareto is noted for his individualistic approach, 10 the latter did not restrain him from granting subjectivity to aggregate entities, which reappeared in the Trattato di Sociologia Generale (1916; 11 hereafter, Treatise) when Pareto deals with the persistence of aggregates. 12 According to the analysis in the Treatise, an aggregate needs at least two constitutive elements. The first of them is the community of sensations/interests as described thus by Pareto (1916: sec. 991): Certain combinations constitute an aggregate of elements closely united as in one body, so that the compound ends by acquiring a personality such as other real entities have. The second is the persistence of those aggregates over time. The feature shared by the individuals constituting an aggregate tends to resist changes, maintaining the aggregate over time. This instinct of preservation is compared by Pareto (1916: sec. 992) to mechanical inertia: it tends to resist the movement imparted by other instincts. This means that relationships between aggregates exist and exhibit some form of subjectivity or individuality, obliging Pareto to refer statistical equilibrium to groups besides individuals: Combinations that disintegrate as soon as they are formed do not constitute groups of subsisting individuality. But if they do persist, they end by acquiring that trait. Not by abstraction only do they take on a sort of individuality, any more than by abstraction only do we recognize groups of sensations by such names as hunger, wrath, or love, or a number of sheep by the name of flock. The point must be clearly grasped. There is nothing corresponding to the noun flock, in the sense that the flock may be separated from the sheep which constitute it. At the same time the flock is not a mere equivalent to the sum of the sheep. The sheep, by the very fact that they are members of the flock, acquire characteristics which they would not have apart from it. (Pareto 1916: sec. 993)

5 Pareto s Social Equilibrium 51 Aggregates and individuals must consequently be analysed as autonomous subjects, although a mutual dependence between them exists: aggregates are composed of heterogeneous individuals. This point clarifies the specificity of Pareto s conception of the aggregate entity: Society as aggregate is different from the individuals forming it, but this does mean that society can exist independently from individuals (Pareto 1905: 296). Some examples of aggregates may aid understanding of this categorisation. Pareto dwelt upon aggregates both with a religious origin, and social classes, as stated in section 1043 of the Treatise. To enlarge Pareto s typology, we can suppose that all cultural, religious, economic, social and cultural features are able to generate an aggregate. The crucial point is the presence of what Pareto calls sentiment, that is, a feeling shared by the aggregate s members. The autonomy of aggregates is obvious when institutions like national governments are considered: 13 in the Manual Pareto (1906: 96) clearly stated this distinction by writing that Governments have quite different ideas about honesty than private individuals have. But this distinction must be analysed in depth when aggregates are spontaneous entities like groups of persons sharing some belief, interest or behaviour. In this sense, these aggregates have a subjective existence that, Pareto (1916: sec. 994) stated, is important for social equilibrium. These entities taken together are not necessarily homogeneous elements but consist of individuals sharing some sentiment or interest; or they simply consist of people who have found some common feature in the past. In all his works, Pareto considered aggregates to be necessary parts of society: A consequence of the heterogeneity of society is that rules of conduct, beliefs, morals, should be, in part at least, different for the different parts of the society in order to obtain maximum utility for the society (Pareto 1906: 95-6). Aggregation occurs on various bases, but it may assume an economic importance. The heterogeneity giving rise to different aggregates is thus a necessary condition for the maximisation of social utility. Aggregates are not sums of their parts but given entities composed of individuals, also independently from their original constitutive cause: The human sentiments of family, so called, of property, patriotism, love for the mother-tongue, for the ancestral religion, for friends, and so on, are of just that character, except that the human being dresses his sentiments up with derivations and logical explanations that sometimes conceal the residue. (Pareto 1916: sec. 1015) In regard to heterogeneity, even though it seems that Pareto conceived this as a feature of human societies due to individual differences, on closer inspection we find that he envisaged different dynamics between heterogeneous individuals and aggregate entities, although the two were intertwined. But it was apparent that social equilibrium could be conceived independently from individual equilibria. Social equilibrium is the result of the interrelation among these aggregates, which include continuously changing groups as well as the social classes theorised by Karl Marx (Pareto 1905: 301). Thus, the assumption of heterogeneity as natural phenomenon obliged Pareto to implicitly recognise two consequences that will be analysed in the next two sections: the first concerns the pertinence of statistical equilibrium to large sets of individuals. This represents the

6 52 History of Economics Review economic application of statistical equilibrium more faithful to statistical mechanics; the second brings Pareto to adapt statistical equilibrium to autonomous groups and to ground social equilibrium on social dynamism. 3 The Statistical Equilibrium of Heterogeneous Individuals In relation to the analysis of heterogeneous individuals by means of statistical equilibrium, Pasquale Jannaccone (1949: 29-30) comments: Pareto s thought oscillates between a representation of social equilibrium as mechanical equilibrium a balance of forces as stated in pure economics, and as statistical equilibrium consisting in continuous balance among the interdependent elements forming a group. Perhaps one depiction may be useful for representing certain problems while the other is useful for others. But, once the social system is considered as a whole, the statistical depiction prevails, as for that matter it does in other fields of the social sciences. The application of statistical tools to the conception of social equilibrium induced Pareto to reflect on the links between individuals and social equilibrium and between aggregates and social equilibrium. The outcome was that while, at that time and with the mathematical tools then at his disposal, it was not easy to go further than the metaphor of gas molecules equilibrium applied to heterogeneous individuals; something more can be ventured on aggregates and social equilibrium. The former type of statistical equilibrium is developed in this section; the latter is considered in the next one. Firstly, Pareto s approach to statistics seemed to be without probabilities. Known statistical methods were introduced in the Cours with some circumspect opening to probabilities: Theory will never be able to tell us what the economic behavior of each individual will be. It will be possible to foresee next year s consumption of alcohol in France; but it will not be possible to foresee the consumption by a given person in a given time. (Pareto : sec. 17) References to probability were paradoxically more frequent in Pareto s first works than in the Treatise. However, we should not forget that Pareto s statistics are grounded on observation. The Treatise makes sporadic reference to probabilities: The field in which we move is the field of experience and observation strictly Every inquiry of ours, therefore, is contingent, relative, yielding results that are just more or less probable, and at best very highly probable. (Pareto 1916: sec. 69) The similarity with the statistical equilibrium in the kinetic theory of gases (Pareto 1916: sec. 2074) was based on the admission that individuals are heterogeneous, but also that their variations offset each other, with the result that the oscillatory states of individuals may result in a general equilibrium (ibid.) and in a stable trend. Thus, the preference for the analogy with the gas theory is just required by the observation that society is composed of molecules more heterogeneous than those

7 Pareto s Social Equilibrium 53 composing the economy, as Pareto stated in section 2079 of the Treatise devoted to the organisation of the social system: The economic system is made up of certain molecules set in motion by tastes and subject to ties (checks) in the form of obstacles to the acquisition of economic values. The social system is much more complicated, and even if we try to simplify it is far as we possibly can without falling into serious errors, we at least have to think of it as made up of certain molecules harbouring residues, derivations, interests, and proclivities, and which perform, subject to numerous ties, logical and non-logical actions. (Pareto 1916: sec. 2079) Individual behaviours are conditioned by existing residues, which may be compared with chemical compounds, and which explain the heterogeneous behaviour of individuals, these latter being likened to gas molecules. Residues do not allow for a logical treatment of social behaviour and, consequently, the extension of economic (mechanical) equilibrium to social facts (Pareto 1916: sec. 2080). Because individual behaviours are conditioned by residues, that is, by sentiments, they are not foreseeable and equilibrium does not have a mechanical nature. But, it is just this cultural feature characterising social molecules that moves Pareto towards the application of statistical equilibrium to groups instead of agents. The cultural dimension of heterogeneity moves the individual towards aggregations becoming the actors of social equilibrium. Continuing with the individualistic representation, the movement towards equilibrium of these chaotic molecules is matched by the idea of moving equilibrium theorised by Pareto in the Manual. One may suppose that the equilibrium state is completely independent of the initial distribution (Bernardelli 1943: 354), consistent with the idea that Pareto s (social) equilibrium has statistical origins. As we will see, social equilibrium exhibits these features: it is a moving equilibrium involving temporary subsequent equilibria. 14 Summing up, a combined reading of the Cours and the Treatise shows that Pareto attempted to treat social equilibrium by adopting a view based on the more probable distribution, thus bringing economics close to Max Planck s nearcontemporaneous innovations in physics. Pareto was not aware that his probabilistic conception of social phenomena might have a correspondence in theoretical physics. This is shown by his sole reference to physicists, particularly to Einstein, in a letter to Maffeo Pantaleoni dated 1921: 15 The Treatise is a very imperfect attempt to introduce into social sciences the notion of relativity that, in a more perfect way, has been introduced in physics. Maybe, in a century, some researchers will discover that at the beginning of the twentieth century an author tried to introduce the principle of relativity into the social sciences. (Pareto 1960: vol. 2, 283) Although it is true that Pareto frequently cited Pierre Simon Laplace and never mentioned Ludwig Boltzmann, he also wrote that economics must be a science of relative, and not absolute, magnitudes, of probable facts and not of certain things (Pareto 1918: 112). However, the idea that different molecules representing heterogeneous individuals could generate social equilibrium was disputed and finally abandoned only in 1922, when Pareto wrote:

8 54 History of Economics Review Society cannot be depicted as a whole composed of separated molecules, where each one acts following its own logic and the general rules; on the contrary, these molecules orbit around certain centers, grouped in specific collectivities, mainly acting and following the logic of sentiments and interests. Social equilibrium springs from the working of all these groups. (Pareto 1922: 1124) Social equilibrium is the product of interrelationships among aggregates or groups of heterogeneous individuals, and not of individuals only, with the consequence that factors explaining aggregation must be singled out. This point requires further attention. 4 Aggregates, Social Dynamism and Social Equilibrium When statistical equilibrium is referred to aggregates, it could be of interest to envisage how aggregates take shape and how they lead the system towards social equilibrium. It was clear to Pareto that heterogeneity involves social consequences, such as an unequal distribution of endowments and wealth, but perhaps it also determines more important effects such as social dynamism. The links between heterogeneity and social dynamism can be grouped into three main types. First, Pareto ( : sec. 658) stated that freedom and heterogeneity are synonymous, but he also recognised that a widespread demand for more egalitarianism may be observed, as shown by this quotation from the Manual: The assertion that men are objectively equal is so absurd that it does not even merit being refuted. On the other hand, the subjective idea of the equality of men is a fact of great importance, and one which operates powerfully to determine the changes which society undergoes. (Pareto 1906: 90) This and other citations suggest that Pareto considered the disposition for homogeneity, and not only heterogeneity, as a fact worthy of analysis. Whatever the origin of heterogeneity, it must be acknowledged that societies tend towards egalitarianism, as upheld a priori by the theology of equality (Pareto 1916: 1896). But, according to Pareto, this non-logical uniformity cannot give rise to a theory. The tendency to homogeneity would mainly characterise the so-called inferiors aggregated in groups or classes: [Equality] is often a defence of integrity on the part of an individual belonging to a lower class and a means of lifting him to a higher one. That takes place without any awareness, on the part of the individual experiencing the sentiment, of the difference between his real and his apparent purposes. He talks of the interest of his social class instead of his own personal interest because that is a fashionable mode of expression. (Pareto 1916: sec. 1220) Groups of individuals claim for more homogeneity. Not only were such classes clearly observable, but in this case their existence appeared to be logical in nature: We can say, if we consider a small, in fact a very small, number of educated people, that in our time there are individuals who come somewhere near the state A; and it may well be though we have no means of proving such a

9 Pareto s Social Equilibrium 55 thing that in the future an even larger number of persons may attain the state A to perfection. (Pareto 1916: sec. 981) Second, it can be deduced that heterogeneity, by providing stimuli to change in social and economic hierarchies, ensures the evolution of societies. Theoretical reasoning or derivations have but little influence on social heterogeneity (Pareto 1916: sec. 2223). On the contrary, heterogeneity is logically explained ex post, when Pareto argues that different economic individuals are needed to provide economic growth, that is, savers, but also adventurous individuals who are forever on the look-out for new combinations, who usually are not savers (Pareto 1916: sec. 2228). If category R comprises rentiers, and category S speculators, Pareto affirmed that: the two groups perform functions of differing utility in society. The S group is primarily responsible for change, for economic and social progress. The R group, instead, is a powerful element in stability, and in many cases counteracts the danger attending the adventurous capers of S s. A society in which R s almost exclusively predominate remains stationary and, as it were, crystallized. A society in which S s predominate lacks stability, lives in a state of shaky equilibrium that may be upset by a slight accident from within or from without. (Pareto 1916: sec. 2235) Pareto found that people are persuaded to deny the existing social heterogeneity by quasi-logical rationalisation. This, notwithstanding differences among economic attitudes, is related to the condition for entrepreneurial activity, and generally for the instinct of combinations that drives the economic system. Third, besides economic differences, the political circulation of élites is a condition for heterogeneity and also its consequence. Pareto followed the same path as pursued in his income analysis: a political élite exists, and like income, it is concentrated in a narrow section of the population. The exercise of power, which no society can do without, involves and at the same time needs, heterogeneity, which, as regards power, becomes hierarchy: Human societies cannot exist without a hierarchy; but it would be a very serious error to conclude from this that they would be more prosperous the more rigid is a hierarchy (Pareto 1906: 313). As usual, Pareto gave historical examples, but he did not look for reasons in history: political difference is a natural aspect of society, and it finds explanation only in the heterogeneity of individual qualities. He wrote: Every people is governed by an élite, by a chosen element in the population; and, in all strictness it is the psychic state of the élite that we have been examining (Pareto 1916: sec. 246). There was only one difference with respect to income distribution: the individuals forming political élites change. Political circulation is more rapid than economic circulation. An essential component of this pattern is the circulation of élites, at various levels. The turnover of governing élites is an outcome of the struggle between groups, but it is also a way to keep conflicts within acceptable levels, giving expression to differences. This is the meaning that can be attributed to the following statement: It is only the accumulation of inferior elements in a social stratum which arms society, but also the accumulation in the lower strata of superior elements which are prevented from rising (Pareto 1906: 288). In the absence of circulation, the social situation may become explosive: When, at the same time, the upper states are full of inferior elements and the lower strata full of superior ones, social equilibrium becomes highly unstable and a violent revolution

10 56 History of Economics Review is imminent (ibid.). Given a conflicting society, representative regimes or democracy are means with which to dampen potential clashes: In virtue of class-circulation, the governing élite is always in a state of slow and continuous transformation. It flows on like a river, never being today what it was yesterday. From time to time sudden, and violent disturbances occur. There is a flood the river overflows its banks. Afterwards, the new governing élite again resumes its slow transformation. The flood has subsided, the river is again flowing normally in its wonted bed. (Pareto 1916: sec. 2056) 16 Pareto stressed the interdependence between heterogeneity and interests, both considered as crucial in forming a society. The protection and safeguarding of specific interests favours the heterogeneous character of society. For example: The dynamic effects of industrial protection enrich not only individuals who are endowed with technical talents, but especially individuals who have talents for financial combinations of gifts for manipulating the politicians who confer the benefits of protection. Some individuals possess such endowments in conspicuous degree. They grow rich and influential, and come to run the country. (Pareto 1916: sec. 2209) Quite paradoxically, according to the Treatise, conflicts originate in the economic area while derivations, ideologies and metaphysical beliefs may contribute to keeping conflicts under control. Not even the establishment of a democratic regime can prevent attempts to gain misappropriations: A political system in which the people expresses its will given but not granted that it has one without cliques, intrigues, combines, gangs, exists only as a pious wish of theorists (Pareto 1916: sec. 2259). All these points show that, when referred to aggregates, heterogeneity is a source of conflicting social relationships that change society. Moreover, whilst nothing can be said about individual forecasts, they are possible in regard to aggregates. 17 Also social equilibrium applied to aggregates took a different, more understandable, meaning than when referred to individuals. Vincent Tarascio (1974: 363) specified this point as follows: Pareto simply generalized Marx s rather narrow and rigid conception of class conflict to include all groups having competing interests and whose existence may vary in duration. The interaction between power and economy is a key to understanding a large part of the Treatise and to explaining Pareto s concern with social heterogeneity (see Pareto 1916: sec. 2238). Consequently, the decisions of economic policy or those concerning national welfare will not be the outcome of an aggregate welfare function: the sum of heterogeneous individual functions is inconsistent. Such decisions will be the result of power relations among lobbies, parties, and institutions influencing government (Pareto 1916: sec. 2130ff). Heterogeneity and the interdependence among individuals and groups give origin to many, sometimes conflicting, movements which fuel the evolution of society. Summing up, differences of abilities, cultures and sentiments produce groups and aggregates which are simply not the sum of representative agents. Rather, the variations in the sub-grouping of heterogeneous individuals into a social aggregate act to stimulate change that must be considered separately from individuals in isolation. Also the then highly criticised social equilibrium should be treated

11 Pareto s Social Equilibrium 57 according to this view: the social system is constantly changing in form (Pareto 1916: sec. 2067). Heterogeneity is the engine of social change. But this continuously changing condition, given the above-mentioned view of moving equilibrium, is a factor of stability and temporary equilibria. As said, the social equilibrium finds its analogue in a statistical equilibrium, grounded on the idea that the variations offset one another (Pareto 1916: sec. 2074); but in this case, the offsetting must be referred to groups. Differences among individuals engender aggregates which allow the system to function and to change. It is clear that social equilibrium involves a condition of temporary equilibrium between two or more social forces or aggregates, but in a process of continuous change. The point is not that social equilibrium could be cyclical or a long-term equilibrium: the point is why social equilibrium is not stationary. The answer lies in heterogeneity and the differences among aggregates. The essence of social equilibrium consists in the process it entails, not in the outcome of the process. 5 Developments of Pareto s Insights A key finding of this paper is that Pareto s interest in statistical equilibrium inspired a remarkable body of literature, mainly during the first half of the century. In particular, the thesis that Pareto anticipated in early twentieth-century economics the revolution subsequently brought about in physics followed two lines of arguments. The first, in accordance with the then emerging quantitative statistics, he focused on the equilibrium of many heterogeneous individuals. Vinci (1924) attributed a wide knowledge of the probability calculus to Pareto, finding in the Cours insights concerning ideas subsequently developed in statistical mechanics. Specifically, there were correspondences between Pareto s arguments and the developments of Boltzmann s analysis put forward by an Italian mathematician, Francesco P. Cantelli (1921), who studied the correspondence between chance and empirical distribution of given phenomena. Vinci concluded that, by admitting certain hypotheses about distribution of individual qualities, one could explain the form of the Pareto income distribution curve. Harro Bernardelli (1943: 355), a German mathematician-economist, reprised Pareto s income distribution. Assuming a probabilistic approach, he tested the supposed stability of that distribution, seeking to demonstrate rigorously that any climbing up or down the social ladder does not take place in chaotic indeterminacy, but that, in a given pattern of society, upstarts and declasses occur, on the average, in definite fixed proportion. Thus, institutional and exogenous rules, more than individual capacities, are supposed to be responsible for the form that the distribution of income takes. The probability that a person may change his/her social position is linked to both an internal factor his/her ability but also to the less or more dynamic character of society. Harold Davis (1949: 249) was persuaded that there was a close and wellgrounded similarity between Pareto s approach to income distribution and Planck s researches on gas distribution in terms, not of application of the kinetic theory of gas to economics, but the use of the same analogies and languages. Raffaele D Addario (1949), an Italian statistician, (and a long series of further authors) interpreted the power law in probabilistic terms. D Addario went further by claiming that there existed a formal parallelism between the equations of

12 58 History of Economics Review the spectral curve representing black hole emissions as studied by Lord Rayleigh (William Strutt) and James Jeans, Wilhelm Wien and Planck, and the income functions formulated first by Pareto and then by Davis. An analogy mainly a formula and representation by means of curves between radiation diffusion at a given temperature, on the one hand, and income distribution, on the other, may be observed. D Addario (1949: 222) wrote: The generative function [to which may be traced back the income curve of Pareto, Lucien March, Jacobus Kapteyn, Vinci, Luigi Amoroso and Davis] comprises in its form a probabilistic distribution equation drawn from the quantum statistics of Brillouin, which in its turn synthesizes and generalizes from a formal viewpoint the quantum statistics of Boltzmann, Bose-Einstein, Fermi-Dirac. Hence the income curve equations may be interpreted, mutatis mutandis, in light of the same probabilistic scheme. The mathematician Benoît Mandelbrot (1963: 259) started from Pareto to challenge the conventional wisdom, stating that the physical phenomena are characterized by the Law of Gauss, and social phenomena by that of Pareto. He did not believe in such a division and showed that the Pareto law could be extended to physical phenomena. 18 Inequality characterises both physical and social phenomena, and this sheds new light upon Pareto s heterogeneity. In 1994, Michio Morishima noted how, on passing from economic equilibrium to social equilibrium, that is, from individuals to aggregates, Pareto s thought was more closely related to the concept of equilibrium in statistical physics. 19 The second line developed the later Pareto view that statistical equilibrium was a metaphor useful to study the equilibrium among groups. This idea was corroborated by the lesser known contributions of Pareto s Italian followers, such as Alfonso De Pietri Tonelli (1931) and Giuseppe Palomba (1935), who applied heterogeneity to different groups forming a society. In both cases, aggregates were built by selecting the characters which were common to large shares of individuals, such as individualists, innovators, conservative people, following De Pietri Tonelli, and selfish or peaceful persons according to Palomba. Those analyses mainly followed sociological patterns, but unfortunately they remained a localised experience. 6 Concluding Remarks The analogies between the economic treatment of aggregates and the treatment of gases and other physical phenomena arising from statistical mechanics did not prevent Pareto from recognising the specificity of social relations. Notwithstanding his efforts to establish a logico-experimental approach to theory, he clearly stated that social molecules may have only a social-economic dimension. In other words, the social equilibrium is the result of interactions among molecules that can be treated scientifically, but which have an economic, moral, intellectual, powerdriven and military dimension (Pareto 1916: sec. 2106). Hence we can establish very general similarities with the hard sciences, and we can borrow methods and tools from mechanics, but we are still concerned with individuals and entities comprising individuals whose behaviour needs social categories for its explanation: interest, sentiment, ambition, and power, as well as altruism and egalitarianism. As pointed out by Samuels (1974: 16-17, 62-7), Pareto was aware of this. Indeed, his entire analysis of heterogeneity may be read as an analysis of power relationships and interdependence. Social dynamism is grounded on power relationships. This is

13 Pareto s Social Equilibrium 59 the world of residues, derivations and, more generally, non-logical actions, complemented by logical ones. From a scientific point of view, this world gives shape to uniformities which can be detected but rarely translated into theory. But it is precisely concepts such as heterogeneity, circulation of élites, and instinct of combinations that enable a dynamic analysis of society and introduce dynamism into the perspective a view that the strict logical theorisations did not permit at the time Pareto was writing. The changing and evolutionary environment, within which sub-aggregates of society operate, is therefore embedded within Pareto s notion of social equilibrium. Consequently, Pareto was not just the ever faithful advocate of mechanistic theory; he also recognised the importance of social dynamics when considering the equilibrium of aggregates. * Department of Economics and Management, University of Padua, via del Santo 33, Padua 35123, Italy. gianfranco.tusset@unipd.it. I am grateful to participants at the 2010 ESHET and 2011 HETSA conferences, where previous versions of this paper were presented, and two anonymous referees for their useful comments. The usual disclaimers apply. Notes 1 Finer, in his (1966) Introduction to Pareto s sociological writings places (social) heterogeneity among the pillars on which Pareto s entire theoretical system is grounded. These pillars also including features such as equilibrium, internal and external forces, élite rule, circulation of élites and economic-cultural cycles are recurring in Pareto s major writings. 2 On the relation between Machiavelli and Pareto see, among others, Marshall (2007: 21 ff). 3 This distinction between the Paretian natural conception of the human being and the Marxian historical conception was also developed by Bobbio (1968: 102 ff.). 4 Residues are not exactly defined by Pareto. They correspond to certain instincts in human beings, and for that reason they are usually wanting in definiteness, in exact delimitation (Pareto 1916: sec. 870). Quoting Pareto, Spengler (1944: 339) wrote that residues correspond to non-logical conduct, are not sentiments or instincts; they are the manifestation of sentiments and instincts just as the rising of mercury in a thermometer is a manifestation of the rise in the temperature. 5 Derivations derive from the residues, but they express the need to clothe them with a logical reasoning. Hence derivations account for the production and acceptance of certain theories (Pareto 1916: sec. 1397). 6 As is well known, as a first approximation, Pareto s law may be expressed as N A x (Pareto ) where N represents the number of income units above a given income threshold; x, A and α are constants. 7 On these aspects see Tarascio (1983; particularly 127-8). 8 See D Amato (1973: 100). 9 The Italian philosopher Norberto Bobbio wrote in 1968 that the Treatise must be considered more than a sociology treatise, a text setting out a general theory on human action where the detailed distinction between different types of action serves as the basis for a theory of ideologies (see Bobbio 1968: 95). 10 See Boland (2003: 32). 11 The 1935 English edition of the Trattato was entitled The Mind and Society: a Treatise on General Sociology.

14 60 History of Economics Review 12 Pareto s idea of aggregate is rather unclear. In the 1935 English edition of the Treatise, the notion of aggregato is translated as group, which must be conceived as an aggregate of sensation (sec. 991, note 1). We partly disagree with the interpretation given in note 1, which does not appear in the original Italian edition, because the aggregate or the group does not involve sensations alone, but the subjective conceptions of group entities or aggregates as well. The persistence of common sensations about some social entities gives form to an aggregate which therefore involves a sort of social identity perceived by each subject belonging to it. It is for this reason that aggregates are so important for social equilibrium. 13 On analysing the relation between individuals and national government, Pareto ( : 80) wrote that individuals do not determine the character of the government, and that the latter does not determine individuals characters. On the contrary, there exists a relation of mutual correspondence between the two subjects. 14 According to this view, Pareto s statement that economic dynamics are possible in sociology only assumes a new meaning. On this point, see Tusset (2009: 275). 15 It is true that relativity is different from probability, but, as D Albergo (1973: 90) argued, Pareto was aware that the laws governing aggregate phenomena, like quantum theory, were statistical in nature. 16 That the political world, besides the economic one, was populated by individuals with different abilities was argued by the Italian economist and philosopher Enrico Leone, who, in 1931, stated that an analogue of the income curve existed also for political and governmental aptitudes (Leone 1931: 51-2). In this case, the upper tail of the curve represents the politicians endowed with more power. 17 See De Pietri Tonelli (1961: 89). 18 Mandelbrot s (1963) approach warrants attention because he reversed the classic relation from natural sciences to social ones, establishing that the Pareto distribution could be extended from the social sphere to physical phenomena. 19 See Morishima (1994: xi). Morishima adds: so it is not an easy thing to achieve a harmonious coexistence between these different equilibria. References Bernardelli, H The Stability of the Income Distribution, Sankhyā: the Indian Journal of Statistics 6 (4): Bobbio, N [1968]. L ideologia in Pareto e in Marx, as repr. in N. Bobbio, Saggi sulla scienza politica in Italia. Roma-Bari: Laterza. Boland, L.A The Foundations of Economic Method: a Popperian Perspective. Abingdon, UK: Routledge. Bordin, A La teoria dell equilibrio e gli schemi probabilistici. Bellinzona: Leins & Vescovi. Cantelli, F.P Sulle applicazioni del calcolo delle probabilità alla fisica molecolare, Metron 1 (1): Castelnuovo, G Calcolo delle probabilità. Milan: Alighieri. Cirillo, R [1974]. Pareto s Law of Income Distribution Revisited, as repr. in Wood and McLure (1999), vol. 4: D Addario, R Ricerche sulla curva dei redditi, in L. Amoroso et al., Vilfredo Pareto: L economista e il sociologo. Milano: Malfasi. D Amato, L L economia del potere. Rome: Esedra. Davis, H.T Pareto statistico, in L. Amoroso et al., Vilfredo Pareto: L economista e il sociologo. Milano: Malfasi.

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