The French Connection: Borda, Condorcet and the Mathematics of Voting Theory – Borda and Condorcet in Later Years

[50] The formation of the National Assembly was instigated by delegates of the Third Estate who were summoned to Versailles by Louis XVI for an emergency meeting of the General Estates, a parliamentary entity that was convened (for the first time since 1614) with the express purpose of securing the necessary approval to enact his government’s tax proposals. Traditionally, each of the three Estates voted as a single group, despite the fact that the Third Estate represented a far greater proportion of the population than either the First or Second Estates, which represented the clergy and the aristocracy respectively. Although members of the Third Estate are generally referred to as “commoners,” its representatives at the Estates General predominantly belonged to the bourgeoisie, particularly the legal professions. After their demand that each deputy instead be given a vote was overruled by a declaration from the First Estate, the representatives of the Third Estate constituted itself as a National Assembly on June 17, 1789; they were later joined in their commitment to create a constitutional monarchy by members of the other two estates.

[51] Like the Declaration of Independence of the United States of America, written some 13 years earlier, primarily by Thomas Jefferson, the Declaration of the Rights of Man and of the Citizen clearly embodies Enlightenment ideals. It begins with a preamble that describes the Assembly’s goal in setting forth a set of “simple and incontestable principles” as an effort to combat the “ignorance, forgetfulness or contempt of the rights of man [that are] the only causes of public misfortunes and the corruption of Governments.” By serving as a unceasing reminder to “all members of the body politic . . . of their rights and their duties,” its authors asserted the desire that “the acts of the legislative power and those of the executive power . . . may . . . be the more respected” and that “the demands of the citizens . . . may always be directed toward the maintenance of the Constitution and the happiness of all.” Jefferson, who was then living in Paris as the US ambassador to France, served as a consultant to those authors, Emmanuel-Joseph Sieyès (1748–1836) and the Marquis de La Fayette (1737–1834), the latter of whom had served as a military consultant to the US during its war of independence from Britain. Unlike the US document, which served in a sense as a rationale for that country’s declaration of war aimed at ousting an oppressor, the French document was initially intended by its authors to serve as a rationale for a transition from an absolute to a constitutional monarchy, rather than an attempt to overthrow the monarchy per se.

[52] The seventeen articles of the Declaration were individually considered and approved by the National Assembly between August 20 and August 26, 1789.

[53] The preamble of the current French constitution still asserts the constitutional status of the Declaration of the Rights of Man and of the Citizen, by declaring that “The French people solemnly proclaim their attachment to the Rights of Man and the principles of national sovereignty as defined by the Declaration of 1789 . . .” [Constitution of the Fifth Republic of France, adopted October 4, 1958].

[54] These complaints were quite literally registered in the Cahiers de Doléances (Complaints Books) that were filed with King Louis XVI (at his invitation) by individuals, trade guilds and legislative units across France in preparation for the 1789 meeting of the General Estates. For example, of the 50 topics found among the complaints submitted by the Third Estate, weights and measures ranked fourteenth [Shapiro et al. 1998, p. 381]. Other frequently mentioned topics of complaint included personal liberties, taxes and the judiciary system.

[55] Condorcet was influential in convincing the National Assembly to approve funding for the Academy in connection with metric reform, although the proposal itself was put before the Assembly by Bishop Charles Maurice de Talleyrand, a former member of the First Estate who aligned himself with the revolutionary cause early on.

[56]According to both [Mascart 1919, p. 497] and [Heilbron 1990, p. 224], the other three members of the Commission on Weights and Measures were initially Jean-Louis Lagrange (1736–1813), the chemist Antoine Lavoisier (1743–1794) and the botanist Mathieu Tillet (1714–1791). After rendering an initial report to the Assembly on October 27, 1790, in which a decimal system was recommended, Lavoisier and Tillet were replaced by Pierre-Simon Laplace (1749–1827) and Gaspard Monge (1746–1818).

[57] The assigned tasks and original working group members were: triangulations and latitude determinations (Cassini IV, Méchain, Legendre), baselines (Meusnier, Monge), pendulum of Paris (Borda, Coulomb), weight of water (Lavoisier, Haüy), and comparison of old and new measures (Tillet, Brisson, Vandermonde). Responsibility for overall supervision of the endeavor was assigned to Borda, Condorcet, Lagrange, and Lavoisier. Two of these four (Condorcet and Lavoisier) died during the Reign of Terror that took place from July 1793 to September 1794. Several members of the original working groups also left the project due to “death and disinclination” [Heilbron 1990, p. 224]. See also [Mascart 1919, pp. 497–500].

[58] Heilbron [1989, p. 991] reports that estimates of the actual amount spent by the Academy to complete the survey range from 300,000 to millions of livres. An additional 500,000 livres in funding was also granted to the Committee of Public Instruction by the National Assembly in order “to defray all expenses relative to the establishment of the new measures, as well as the advances which are indispensable for the success of such work,” as stipulated in Article 21 of a National Assembly decree approved on April 7, 1795.

[59] Some have suggested that the Commission’s decision not to instead define the meter as the length of a pendulum with a half-period of one second (called a seconds pendulum) was due to an interest within the Academy in seeing a demonstration of the accuracy of Borda’s repeating circle. See, for instance, [Hahn 1971, p. 164].

[60] The full text of the legislative acts related to the official adoption of the metric system in France can be found in a report on the question of adopting the metric system in the United Kingdom that was later commissioned by Queen Victoria [Airy et al. 1869].The French decree of August 1, 1793, that legally adopted the metric system as that nation’s official system of weights and measures also mandated its obligatory use beginning July 1, 1794. In a new decree approved on April 7, 1795, the latter provision was rescinded indefinitely, due in part to the reluctance of the public to abandon its use of the existing units of measurements. (That same decree also indefinitely suspended the 1793 provision requiring the use of the decimal division of the day and the parts thereof.) Historian of science Kenneth Alder has offered a convincing explanation for why there was such resistance to actually using the metric system, despite the fact that it was complaints from the French people themselves that helped bring the new system into existence [Alder 1995; Alder 2002]. His book, The Measure of all Things: The Seven Year Odyssey and Hidden Error that Transformed the World [Alder 2002], also provides a riveting account of the surveying project behind the definition of the meter.

Figure 7: Woodcut dated 1800 illustrating the new decimal units which became the legal norm in France on November 4, 1800, five years after the metrical system was first introduced. In the captions, each one of these six new units are followed by the old French unit in brackets.These were for length (metre), area (are = 100 m2), solid volume (stère = 1 m3), liquid volume (litre = 1 dm3), mass (gramme = the mass of 1 cm3 of water) and currency (franc). Wikicommons.

[61] In the original French: “Une bonne loi doit être bonne pour tous les hommes, comme une proposition vrai est vrai pour tous.” Condorcet wrote his “Observations de Condorcet sur le vingt-neuvième livre de "L'esprit des lois" (”Observations on the twenty ninth book of “Spirit of Laws”) in 1780 as a commentary on a highly influential political theory treatise by Charles de Secondat, Baron de Montesquieu (1689–1755), De l'esprit des loix (The Spirit of the Laws), originally published anonymously in 1748. The publication details of Condorcet’s essay are not fully clear. It was not included in the 1804 edition of Condorcet’s collected works, but does appear in Volume 1 of the 1847 edition [Condorcet 1847, pp. 363–388]. In the intervening years, Condorcet’s essay appeared in its entirety in Thomas Jefferson’s 1811 English translation of de Tracy's Commentaire sur l'Esprit des Lois de Montesquieu par M. le comte de Destutt de Tracy (A Commentary and Review of Montesquieu's Spirit of Laws) [de Tracy 1811], and in the later French editions of that same work [de Tracy 1817; de Tracy 1819]. Antoine Louis Claude Destutt, comte de Tracy (1754–1836) was a French philosopher who is credited with coining the term "ideology" while being held in prison during the Reign of Terror.

[62] Condorcet wrote several essays advocating the abolition of slavery, the first of which, “Reflexions sur l’esclavage des nègres” (“Reflections on the enslavement of negros”), was published well before the revolution, in 1781. He was also a founding member, along with the military commander La Fayette, of the Société des Amis des Noirs (Society of the Friends of Negros), established in 1788. His 1790 essay, “Sur l’admission des femme au droit de Cité” (“On the admission of women to the right of Citizenship”), further argued the ability to reason, a human attribute shared by men and women of all races, justifies granting equal rights to all:

The rights of men stem exclusively from the fact that they are sentient beings, capable of acquiring moral ideas and of reasoning upon them. Since women have the same qualities, they necessarily also have the same rights. Either no member of the human race has any true rights, or else they all have the same ones; and anyone who votes against the rights of another, whatever his religion, colour or sex, automatically forfeits his own.

[63] The plan for state-supported education that Condorcet helped to draft formed the basis of the national educational system that was eventually adopted, which in turn led to the creation of the École normale supérieure and the École centrale des travaux publics (later called the École polytechnique).

[64] The Royal family had been essentially under house arrest at the Palace of the Tuileries in Paris since the so-called Women's March on Versailles took place on October 6, 1789, in part as a reaction to the chronic hunger and increasing frustration brought about by the costs and scarcity of bread in the city. Concerns about Louis XVI’s intentions became more pronounced following his family’s aborted attempt to flee the country during the night of June 20–21, 1791. Nevertheless, the National Constitutional Assembly was willing to allow Louis to retain the throne under a constitutional monarchy at that time. According to the nineteenth-century historian François Auguste Marie Mignet (1796–1884), after Louis XVI examined the Assembly’s 1791 constitution, he sent a letter to the Assembly in which he wrote: “I accept the constitution. I engage to maintain it at home, to defend it from all attacks from abroad; and to cause execution by all the means it places at my disposal. I declare, that being informed of the attachment of the great majority of the people to the constitution, I renounce my claim to assist in the work, and that being responsible to the nation alone, no other person, now that I have made this renunciation, has a right to complain” [Mignet 1846, p. 110]. The Assembly is then reported to have subsequently invited Louis XVI to address their final session on September 29, 1789, where the King pronounced: “Tell [your fellow citizens] that the king will always be their first and most faithful friend; that he needs their love; that he can only be happy with them and by their means; the hope of contributing to their happiness will sustain my courage, as the satisfaction of having succeeded will be my sweetest recompence” [Mignet 1846, pp. 110–111].

[65] Although opposed to the death penalty on principle, Condorcet did not vote against the death penalty for Louis XVI, but instead chose to abstain. The abolition of the death penalty was, however, one of the 370 articles in Condorcet’s proposed version of the new constitution. In his 1791 “Opinion sur le jugement de Louis XVI” (“Opinion on the trial of Louis XIV”), a copy of which was owned by Thomas Jeffereson, Condorcet also presented his probabilistic view of voting to argue against executing the King.

[66] While the politics of the French revolution are too complex to recount here, the description of Condorcet’s abilities (or lack thereof) as a politician offered by historian John Herivel suggest another possible factor in the failure of Condorcet’s constitution [Herivel 1975, p. 247]:

Condorcet was no politician. His uncompromising directness of manner and inability to suffer illogical windbags in silence made him many enemies and few friends. His weak voice, lack of oratorical powers, and tendency to bore the Convention by the excessive height of his arguments was one of the tragedies of the Revolution.

[67] The Committee of Public Safety was actually created in April 1793, to replace the previous Committee of General Defense, an administrative body that was charged with protecting the new republic from internal and external attacks. In July 1793, Robespierre (1758–1794) became a member of the restructured Committee of Public Safety and served as its de facto leader until his own arrest and subsequent death by guillotine a year later essentially brought the Reign of Terror to a close.

    Interestingly, the mathematician and military engineer Lazare Carnot (1753–1823) served as a member of the Committee of Public Safety from September 1793 until it was disbanded in March 1795. As a relatively conservative member of the committee, Carnot concentrated primarily on issues related to education and military operations. From 1795 to 1797, he continued to provide military leadership for the country as an elected member of the Directory, the five-member executive branch of the re-organized government that ruled France immediately following the dissolution of the Committee of Public Safety. As the Director in charge of military affairs, it was Carnot who appointed Napoléon Bonaparte (1769–1821) as general-in-chief of the Army of Italy. When Napoleon declared himself emperor of France in 1804, the republican-minded Carnot retired from public life. He lived out his final days in exile from France, devoting his energies to writing works on engineering and geometry.

[68] Estimates of the number of individuals that were executed in France during the Reign of Terror by the guillotine or other means range upwards of 17,000, excluding those who died at the hands of vigilantes or in prison while awaiting their trial. Lynn, who sets the number of official executions at 40,000, further estimates that the number of individuals who were arrested accounted for about 1 in every 50 French citizens, or approximately 300,000 individuals in all [Lynn n.d.]. Members of the clergy and aristocrats were disproportionately represented both among those arrested and those executed by the state.

[69]Located on Paris’ left bank on the Rue des Fossoyeurs (now 15 Rue Servandoni), Condorcet’s refuge for these months is situated just behind the beautiful Église Saint Étienne de Mont, where Blaise Pascal (1623–1662) is buried. Coincidentally, Olympe de Gouges (1745–1793), a playwright and author of the Declaration des Droites de Femmes et Citoyennes (Declaration of the Rights of Women and Citizenesses), lived on this same street, within half a block of Condorcet’s hiding place. Although it is unlikely that they associated with each other during this time, the two were almost certainly acquainted, given De Gouges’s attendance at the salon of Condorcet’s wife Sophie de Condorcet, née de Grouchy, at the Hôtel des Monnaies. Condorcet only met his protector Madame Vernet, the widow of the sculptor Louis-François Vernet (1744–1784), when mutual friends brought him to her home seeking refuge.

[70] Condorcet’s Esquisse was published posthumously by his wife, Sophie de Condorcet, née de Grouchy, in 1795. In 1799, she also published his Éloges des academicians (Eulogies for the Academicians). Although de Grouchy had filed for divorce while Condorcet was in hiding, she did so with his secret consent as a move to prevent the seizure of her property by the revolutionary government due to her marital connection to the fugitive Condorcet. This strategy failed when he died before the divorce was finalized. De Grouchy thereafter earned a living for herself and their daughter Eliza by painting miniature portraits. She also continued to edit Condorcet’s collected works, and remained active in France’s intellectual culture through her re-established salon. Although de Grouchy wrote many articles that were published anonymously, both before and after the revolution, the only one of her works to appear in her own name was the book Huit Lettres sur la Sympathie (The Letters on Sympathy), which was published alongside her translation of Adam Smith’s Theory of Moral Sentiment and Origins of Language in 1798.

[71] Located at 49 Grande Rue (now 81 Ave Le Clerc), the lower floor of the house in which Condorcet spent his last night was being used as a hair salon in 1999 when the author took the following photo (Figure 8).

[72] At the time, the town was called “Bourg-de-l’Égalité.” Bourg-la-Reine is also familiar to students of the history of mathematics as the birthplace of Évariste Galois (1811–1832), known both for his contributions to algebra and as a staunch supporter of the French republicans during the post-Napoléonic era.

[73] Although the location of his remains is also unknown to this day, memorials of Condorcet’s life and work include plaques at his final “residences” in Paris and Bourg-la-Reine, a statue at 15 Quai de Conti in Paris (between the Musée de Monnaie and the Institut du France), and the symbolic interment in the Pantheon in Paris of ashes taken (in 1989) from the cemetery in Bourg-la-Reine.

[74] Memorials of Borda’s life and work include a statue in the Place de la Halle in his birthplace of Dax, and a series of French naval vessels harboured in Brest (and nicknamed The Borda) that have successively served as the site of French Naval School since its founding in 1830. The current collection of scientific instruments and other objects in the Borda Museum in his hometown of Dax was founded on Borda’s own collection of curiosities. Borda’s name (but not Condorcet’s) is also listed, together with 71 other scientists, on the first floor of the Eiffel Tower. Both men have Paris streets named after them (Borda in the 3rd Arrondisement and Condorcet in the 9th).