Marie Jean Antoine Nicolas Caritat, marquis de Condorcet (1743–1794), was a French mathematician, philosopher, and politician, the author of a philosophy of progress, of a program for educational reform, and one of the first to apply the calculus of probabilities to the analysis of voting and to social phenomena in general. He was among the most original thinkers of the revolutionary age.
Born at Ribemont in Picardy, Condorcet had a brilliant scholastic career with the Jesuits at Rheims and at the Collège de Navarre in Paris. He attracted the attention of such mathematicians as d'Alembert, Clairaut, Fontaine, and Lagrange, although his mathematical publications had no permanent importance. At the same time he attended the salon of Mile, de Lespinasse, became a friend of Turgot's, and, with d'Alembert, made a pilgrimage in 1770 to Fernet to see Voltaire. He remained on excellent terms with Voltaire. He married Sophie de Grouchy in 1787; their salon at the Hôtel des Monnaies became one of the most brilliant in Paris.
Condorcet pursued three careers simultaneously and with varying success—an academic one, an administrative one, and a political one. As assistant to the secretary of the Académic des Sciences from 1769 on, he wrote a large number of éloges and recorded proceedings; he was elected a member of the Académic Française in 1782. As an administrator, he was appointed inspecteur des monnaies in 1774 and entrusted with various scientific missions by Turgot, then the minister of finance. Finally, in the context of politics, he drew up, in 1789, the petition of the nobility of Nantes (one of the cahiers de doléances). As a deputy to the Legislative Assembly, he was an active member of the Committee on Public Education. After being elected to the Convention, he was chosen to prepare the Girondist draft for the constitution, but although his proposals were almost always passed on the floor, they were very rarely put into effect. In 1793 he shared the fate of the Girondins: his arrest was ordered in July 1793, but he managed to remain hidden in Paris until March of the following year; then he was arrested, and he died under mysterious circumstances in the prison of Bourg la Reine.
An enlightened nobleman. Prominent in scientific, political, and worldly circles, Condorcet is a typical example of the enlightened segment of the nobility that supported the Revolution. He was one of the first to be converted to the idea of republicanism. His ideology of social progress, his economic liberalism, and his faith in the omnipotence of rational knowledge allied him with the rising bourgeoisie rather than with his own class.
Condorcet might well be called the last of the Encyclopedists. He took an active part in the publication of the Supplément à I'encyclopédic, and more particularly in recasting its mathematical portion, the Encyclopédic méthodique, in 1784–1785. His curiosity was universal, and his most characteristic effort was his attempt to join and coordinate mathematics and philosophy and thus “satisfy two passions at once,” as he wrote to Frederick the Great. He considered philosophy to include everything relating to the knowledge of man: “the metaphysical and social sciences, those that have man himself as their object …” (1847–1849, vol. 6, p. 494). His epistemological principles were borrowed from Condillac, but Condorcet differed greatly from Condillac in his conception of man's destiny and the fate of human societies.
Condorcet's best-known work, the Sketch for a Historical Picture of the Progress of the Human Mind (1795), was written while he was in hiding in Paris in 1793–1794. In it he presented a history of the errors and the advances of humanity, in order to predict, direct, and accelerate its forward march. In Condorcet's view, historical development coincides with the spread and triumph of the light of reason.
Condorcet believed that education, more than anything else, produced the triumph of the Enlightenment. He regarded inequality of education as one of the main sources of tyranny and advocated public education that would offer to all who might benefit from it the “aid hitherto confined to the children of the rich.” Nonetheless, his interests remained those of the bourgeoisie and the enlightened nobility, and his educational recommendations consist, in effect, of two separate programs based on class distinctions; one is for the lower classes and is essentially technical; the other is for the ruling classes and develops the critical faculties of future citizens.
“Social mathematics.” An essentially new feature of Condorcet's educational program was the importance he gave to science at every level of instruction, in particular to applied science. In addition, he believed that the social sciences should be taught in institutes and lycées. One of his central ideas is the importance to the progress of humanity of developing an “art of society” (art social).
In essence, Condorcet conceived of this art social as an “application of mathematics to the moral sciences,” a discipline at once empirical and deductive, making use of genuine mathematical models of human phenomena. Condorcet was convinced that “the truths of the moral and political sciences can be as certain as those that make up the system of the physical sciences” (1785, p. 1). However, he believed that this certainty generally does not apply to causal relationships but to probable connections. The primary concern of what he called “social mathematics” is the application of the calculus of probability to the description and prediction of human phenomena.
This mathematics, as it emerges in Condorcet's published writings and unpublished manuscripts, comprises a statistical description of societies, an economic science (physiocratic in inspiration, but oriented toward the more recent idea of collective welfare), and a combinatory and probabilistic theory of intellectual operations.
This last theory appears in connection with the theory of voting, which is by far the best-developed part of social mathematics (1785). Voting was viewed by Condorcet as making manifest not so much a compromise among a number of conflicting forces as a true opinion. He assumed, therefore, that the question being voted on has a true solution that is independent of the wishes of those voting and that these voters express in their individual choices their greater or lesser understanding of that truth. The problem of structuring the process of voting is that of producing the maximum probability of a collective choice of the true solution; this may be done by varying the size of the voting body and the kind of majority required, as well as by considering the likelihood that each voter will make a correct decision. Condorcet was thus led to the construction of statistical models of voting bodies that permit the appraisal of the probability that collective decisions will correspond to the true answers to particular problems. This is, then, a real problem in operational research—how to establish voting procedures such that the chances of the emergence of correct decisions are maximized.
Since he conceived of voting as a collective search for the truth, Condorcet had to deal with the problem of defining precisely what a collective decision or judgment is. Given a series of dichotomous questions, the “yes” or “no” responses to them may be called “judgments”; how, then, may a single collective judgment or a coherent hierarchy of judgments be established on the basis of a set of individual judgments? Charles de Borda, 1733–1799, had shown that in the choice of the “best” among three candidates the one so designated by a simple majority might not be the same as the one arrived at when each is compared with the two others. Condorcet showed that such a weighing of preferences may reveal a circular order of preferences among the candidates— A> B > C > A—and, consequently, the possibility of an inconsistent collective choice even when individual choices are consistent. The mathematical apparatus available to Condorcet was too crude for him to obtain results that could be applied empirically, but he did open the way to a highly original and important social scientific conception.
Influence. The ideology of progress of Condorcet's Esquisse directly influenced Auguste Comte. His influence on the application of mathematics to human affairs can be found in such nineteenth-century works as those of Poisson and Cournot. The questions involved in the formation of a collective opinion have quite recently been taken up again by, among others, K. J. Arrow and G. Th. Guilbaud, although they have been reformulated in the light of welfare economics and the theory of games.
1785 Essai sur I'application de I'analyse à la probabilité des décisions rendues à la pluralité des voix. Paris: Imprimerie Royale.
(1795) 1955 Sketch for a Historical Picture of the Progress of the Human Mind. New York: Noonday. → First published as Esquisse d'un tableau historique des progrès de l'esprit humain.
1847–1849 Oeuvres. 12 vols. Edited by A. Condorcet O'Connor and M. F. Arago. Paris: Firmin-Didot.
Arago, FranÇois 1879 Condorcet: A Biography. Pages 180–235 in Smithsonian Institution, Annual Report of the Board of Regents, 1878. Washington: The Institution.
Cahen, LÉon 1904 Condorcet et la révolution française. Paris: Alcan.
Granger, Gilles-Gaston 1956 La mathématique sociale du marquis de Condorcet. Paris: Presses Universitaires de France. → Contains a comprehensive bibliography of Condorcet's mathematical works.
Guilbaud, Georges Th. 1952 La théorie de l'intérêt général. Economic appliquee 4:501–584.
Todhunter, Isaac (1865) 1949 A History of the Mathematical Theory of Probability From the Time of Pascal to That of Laplace. New York: Chelsea.