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1 Georges-Théodule GUILBAUD Theories of the General Interest and the Logical Pr

1 Georges-Théodule GUILBAUD Theories of the General Interest and the Logical Problem of Aggregation English translation of “Les théories de l’intérêt général et le problème logique de l’agrégation” Economie appliquée, volume V no 4, Octobre-Décembre 1952, pp.501-551. 1 Theories of the General Interest, and the Logical Problem of Aggregation1 G. Th. Guilbaud2 "Le peuple a les opinions très saines; par exemple: (…) travailler pour l’incertain; aller sur la mer (…)." "Or, quand on travaille pour demain et pour l’incertain, on agit avec raison car on doit travailler pour l’incertain, par la règle des partis qui est démontrée. Saint Augustin a vu qu’on travaille pour l’incertain sur mer, en bataille etc, mais il n’a pas vu la règle des partis qui démontre qu’on le doit."3 (The opinions of the people are very sound; for example: (…) they work for uncertain things, they go out to sea ( …). Now, when one works for tomorrow and for something uncertain, one behaves reasonably, because one should work for uncertain things according to the rule of departing the stakes which has been proved. Saint Augustin had seen that people worked for uncertain things, on the sea, in battles, etc., but he had not seen this rule which proved that one should do this.) We know that this rule is the point of departure, not only for the technique that ultimately came to be known as probability calculus, but also and mainly for the use of mathematics in the study of human actions. "Opinions du people saines" (Sound opinions of the people) notes Pascal; a century and a half later. On the same topic, Laplace reiterates this idea in the conclusion of his Essai philosphique sur les probabilités : "La théorie des probabilités n’est, au fond, que le bon sens réduit au calcul : elle fait apprécier avec exactitude ce que les esprits justes sentent par une sorte d’instinct, sans qu’ils puissant souvent s’en rendre compte4." (Fundamentally, probability theory is just common sense condensed in computations: it assesses in an exact manner what sound minds feel by a kind of instinct, often without being aware of it.) But then why should we bother with tiresome computations if these only confirm common sense? Laplace explains himself through the example of mathematical theory applied to the moral sciences: "On a encore soumis au calcul la probabilité des témoignages, les votes et les décisions des assemblées électorales et délibérantes et les jugements des tribunaux. Tant des passions, d’intérêts divers et de circonstances compliquent les questions relatives à ces objets, qu’elles sont presque toujours insolubles. Mais la solution de problèmes plus simples et qui ont avec elles beaucoup d’analogies, peut souvent répandre sur ces questions difficiles et importantes, de grandes lumières que la sûreté du calcul rend toujours préférables aux raisonnements les plus spécieux."5 (Once more we have been able to compute the probabilities of testimonies, votes and decisions of electoral and deliberating assemblies and court rulings. Strong feelings, diverse interests and circumstances complicate the questions related to these situations to the point where they are almost always impossible to solve. But the solutions to simpler problems provide us with many analogies that may shed much light on these difficult and important questions in a way that is, due to 1 English translation of “Les théories de l’intérêt général et le problème logique de l’agrégation” Economie appliquée, volume V no 4, Octobre-Décembre 1952, pp.501-551. 2 1911-2007. See biography and publications in Mathématiques et Sciences humaines (184, http://www.ehess.fr/revue- msh/recherche_gb.php?par=numero). 3 Pascal, Pensées, nos 324 and 234, in the Brunschwig edition, nos 101 and 577 of Lafuma. 4 Oeuvres de Laplace, édition nationale Paris, 1847, v. VII, p.169. 5 Laplace, Essai philosophique sur les probabilités (1812); Introduction à la théorie analytique des probabilités , Œuvres, Paris, 1847, v. VII, p.164. – 2 – the certainty of computation, always preferable to the most specious reasoning). What is important is "d'apprendre à se garantir des illusions qui souvent nous égarent" (to learn how to guard ourselves against the delusions that often lead us astray). The analysis of mechanisms of collective choice provides a beautiful example of this use of mathematics: it is easy to draw a parallel between the recent scholarly works on Welfare and the intuitions of Hobbes and Rousseau concerning the general will — and if one is so inclined, to marvel at the considerable efforts required to show what many very bright minds held for obvious. However, Laplace was not mistaken, the computations were not made in vain — to the extent that they dispersed some delusions and brought about a revival of a very ancient topic of study. * * * Throughout the XVIII century, it is under the heading of probability calculus that we find almost all attempts to mathematically analyze human problems. This is mainly due to the fact that the initial influence from Pascal had persisted: one attempts to elucidate not only the conduct of players properly speaking but also that of man struggling against uncertainty. But it is also because the last thing that one finds when making a work is the one that should be placed first. For a student today, the theory of choice appears to be much simpler than that of games: first one reasons, following Pareto, by completely eliminating risk and uncertainty to attain pure choice. But the first researchers did not attack the problems that we consider today to be the simplest ones. Here, as in many other domains whether or not they are mathematical, thinking advances in two directions: by combining it explores consequences but it also traces its way back towards the principles ; beginnings can never be really elementary. And thus, choice theory, in its early days, emerged from the reflections on two types of problems considered today to be complicated: firstly, choice under uncertainty and secondly the choice of a collectivity. The first theme, that of uncertainty prompted Daniel Bernoulli and Buffon to sketch the first drafts of a theory of total or marginal utility, given the name of a theory of "moral values". The second theme, that of collective decisions and conflicting wills is no less important: the non comparability of utilities and the major difficulties of expressing a collective will were analyzed by Condorcet, Laplace and some others6. But if we take Buffon’s Arithmétique morale or Condorcet’s Mathématique sociale as our point of departure then there is no continuous tradition that traces a path all the way to the New Welfare Economics: there is a deep divide within the history: Cournot and Poisson were the last representatives of a style that would be ignored or mocked at for a century, whereas Walras or Pareto, to mention only eponymous heroes, hardly considered themselves as the heirs of the social mathematicians of earlier times. When speaking of the history of mathematical economics or econometrics, it used to be common practice to present Cournot as its founder or precursor.7 Precursor, one could say that, in the sense that it is today that it becomes possible to grasp the significance of his work (by adding to his works in economics strictly speaking his book on The theory of chance, and just as importantly his philosophy of history) but we should not imagine that there were a straight path between him and us — rather there were long detours and much narrow- mindedness. 6 Concerning Condorcet, one should read: La mathématique sociale du marquis de Condorcet (The social mathematics of the marquis Condorcet), by G.G. Granger, Paris, P.U.F., 1956. 7 But cf. Tinbergen, Econometrics, Philadelphia, 1951, p. 9. – 3 – With the superficial sarcasms that he directed at Cournot and Laplace, Joseph Bertrand attacked what was already an old tradition. In an ill-tempered and rather unintelligent manner he was persuaded that everything was almost over, that enlightenment would definitely condemn a temporary straying from the right path and that probability calculus would reject its impure origins to concern itself only with the material world of physics or biology, leaving the "moral" universe to rely on "common sense" alone to avoid "delusions". It is true that the ambitions of certain scholars had been immoderate and that their foolhardiness or the inflexibility of preconceived mathematical tools would discredit them in the eyes of an unprepared opinion. How could we not be worried by the title of Poisson’s work8: Recherches sur la probabilité des jugements en matière criminelle et en matière civile, précédées des règles générales du calcul des probabilities? (Research on the probability of judgments in criminal and civil cases, preceded by general rules of probability calculus) But "ceux que nous appelons anciens étaient véritablement nouveaux en toutes choses et formaient l’enfance des hommes proprement"9 (those who we call old were actually new in every way and really formed the childhood of later men…). Altogether, there is perhaps nothing to regret. Progress is not linear and some books must wait a long time before they are truly and actively read. * * * The profound studies of K.J. Arrow brought uploads/Philosophie/ guilbaud.pdf