Abstract
Marie Jean Nicolas Caritat, Marquis de Condorcet (1734–1794) was a man of polymathic, if not polyhistoric, proportions. Pearson [1978] has described him as follows:
there have been better mathematicians, better economists, better historians, better philosophers and better politicians than Condorcet, but scarcely any man has been at the same time as good a mathematician, as good an economist, as good an historian, as good a philosopher and as good a politician as he was. [p.425]
The Productions of an exalted Genius are very liable to Misconstruction and Cavil, as the Subject is often clouded with some natural Intricacy.
Francis Blake.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Notes
For a general discussion of Condorcet’s work see Gouraud [1848, pp.89–104], Maistrov [1974], Pearson [1978] and Todhunter [1865]. For a brief discussion of his work on probability see Baker [1975, p.81].
Gillispie [1972, p.15], writing of the memoir, says “It will hardly be worth while to follow him in these writings obscurely expounding the reasonings and procedures of probability itself in relation to causality and epistemology” Recent work by Crepel, however, has been devoted to denying, if not indeed refuting, the existence of such obfuscation (see in particular his [1988a], [1988b], [1989a] and [1989b], and Bru and Crepel [1989]).
See Laplace’s Mémoire sur les probabilités, and also Todhunter [1865, art.773] and Trembley [1795–1798].
Condorcet’s rebarbative notation has been altered and some obvious misprints have been corrected.
Translated by Pearson [1978, p.456] as “between two contingent events becoming actual”.
Various other “multiple Bayes’s integrals” are given, but this illustrar tion is sufficient.
The reference is to Laplace’s Sur les approximations des formules qui sont fonctions de très grands nombres of 1782.
See Pearson [1978, p.457].
For further comments on Condorcet’s failure to mention Bayes see Stigler [1975, p.505]. Note also Pearson [1978, p.181].
The persistence of this habit to this day is remarked on by Neveu [1965, p.ix].
Todhunter [1865, art.734] has “the next p + q trials”, as does Pearson [1978, p.458]: the adjective is not present in the original, though this was probably the intent.
For further details see the preface to Pearson [1978].
See Dale [1982].
For some comments on Condorcet’s work on testimony see Zabell [1988b].
For further examination of this formula see Owen [1987, §3], Sobel [1987, §2] (where the Bayes-Laplace rule is recast as “The Hume-Condorcet Rule for the Evidence of Testimony”) and Todhunter [1865, art.735].
This sixth part is discussed in some detail in Todhunter [1865, arts 737–751].
For an opinion in turn on Gouraud’s exuberance see Todhunter [1865, art.753]. The awkwardness of Condorcet’s expression seems to have manifested itself early in his career. According to Baker [1975, p.6] the first paper submitted to the French Academy of Sciences was rejected by Clairaut and Fontaine, who had been charged with its examination, on account of “its sloppiness and its lack of clarity”.
See Todhunter [1865, art.467].
Hacking [1971, p.351] considers no phrase in our subject “less felicitous” than Condorcet’s probabilité moyenne.
Similarly harsh sentiments have been expressed by Bertrand, who, in commenting on Condorcet’s Essai, wrote “Aucun de ses principes n’est acceptable, aucune de ses conclusions n’approche de la vérité” [1972, p.319]. Gillispie [1972, p.12], on the other hand, describes Todhunter’s judgement as “harsh”, and he provides some comments by Condorcet’s contemporaries as evidence of the esteem in which he was held.
See Hacking [1971, p.351].
Hacking [1971, p.351] considers Condorcet as the first to render explicit the “groping for the idea of probability as ‘judgement’ or credibility.” For comments on the distinction between “logical” and “physical” probabilities to be found in the works of D’Alembert, Condorcet and Laplace, see Baker [1975, pp.177–178].
Condorcet describes the third part of this work as an “Ouvrage plein de génie & l’un de ceux qui sont le plus regretter que ce grand homme ait commencé si tard sa carrière mathématique, & que la mort l’ait si-tôt interrompue” [p.viij].
See Gillispie [1972, p.15].
Writing of the use of Bayes’s Theorem in the probability of judgements, Poisson [1837, p.2] says “il est juste de dire que c’est à Condorcet qu’est due l’idée ingénieuse de faire dépendre la solution, du principe de Blayes [sic], en considérant successivement la culpabilité et l’innocence de l’accusé, comme une cause inconnue du jugement prononcé, qui est alors le fait observé, duquel il s’agit de déduire la probabilité de cette cause.”
Perhaps one sees here an adumbration of the Principle of Irrelevant Alternatives.
For a summary of the Essai see Cantor [1908, pp.253–257].
As precursors in the search for a method for the determination of the probability of future events from the law of past events Condorcet cites Bernoulli, de Moivre, Bayes, Price and Laplace [p.lxxxiij].
In Condorcet’s notation, \(\left( {\begin{array}{*{20}c} {m + n} \\ n \\\end{array}} \right)\) is written \(\frac{{m + n}}{n}\) In Problem 3, however, \(\frac{1}{0}\) is used to mean “infinity”. This is a prime example of what Todhunter [1865, art.660] describes as Condorcet’s “repulsive peculiarities”. Pearson [1978, p.480] argues that the curve of judgements should be of the form y0(x − ½)p(1 − x)q.
See Dinges [1983, pp.68, 95] for comment on the occurrence of this result in Condorcet’s work.
The integrand in the second integral is given by Condorcet as (1−x)n.
Todhunter [1865, art.698].
Here we have another example of Condorcet’s awkward notation: the integral \(\int_{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}}^1 {x^m \left( {1 - x} \right)^n } \) is written as \(\int {\frac{{\frac{1}{2}}}{{x^m \left( {1 - x} \right)^n }}} \) in the original.
As Todhunter [1865, art.701] points out, Condorcet ought to say “let the probability not be assumed constant”.
It is this result that Pearson [1978, p.366] describes as “really Condorcet’s and Laplace’s extension of Bayes.”
The factor \(\left( {\begin{array}{*{20}c} q \\ {q'} \\\end{array}} \right)\) is missing in the original.
For a general discussion of Condorcet’s application of probability to the voting problem see Gillispie [1972, p.16]: Auguste Comte’s opinion on the matter is discussed in Porter [1986, p.155].
See Pearson [1978, pp.482–489] for a discussion of Parts 4 and 5. A general discussion of the probability of decisions, with special reference to the work of Condorcet, Laplace and Poisson, may be found in Chapter XIII of Bertrand [1972].
For a general discussion of this paper see Pearson [1978, pp.501–505].
Two of which are numbered VI.
“Qui a pour objet l’application du calcul aux sciences politiques et morales” [p.171].
These two articles are respectively entitled “De l’intérêt de l’argent” [pp.2–31] (the first page is an introduction) and “Sur une méthode de former des tables” [pp.31–56]. See Crepel [1988a] for a discussion of these articles.
For reference to earlier work on testimony by John Craig (d.1731) see Pearson [1978, p.465] and Stigler [1986c].
On this point see Pearson [1978, p.502].
The first Article VI (see Note 40 above) is entitled “Application du calcul des probabilités aux questions où la probabilité est déterminée” [pp.121–145]; the second is “De la manière d’établir des termes de comparaison entre les différens risques auxquels on peut se livrer avec prudence, dans l’espoir d’obtenir des avantages d’une valeur donnée” [pp.145–150], while the seventh article is “De l’application du calcul des probabilités aux jeux de hasard” [pp.150–170].
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1991 Springer-Verlag New York, Inc.
About this chapter
Cite this chapter
Dale, A.I. (1991). Condorcet. In: A History of Inverse Probability. Studies in the History of Mathematics and Physical Sciences, vol 16. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-0415-9_5
Download citation
DOI: https://doi.org/10.1007/978-1-4684-0415-9_5
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4684-0417-3
Online ISBN: 978-1-4684-0415-9
eBook Packages: Springer Book Archive