Abstract
Systematic theorizing on elections was part of the general uprush of thought in France in the second half of the eighteenth century. The first thinker to develop a mathematical theory of elections was Borda, a member of the Academy of Sciences. In the course of a busy life in which he was successively an officer of cavalry and a naval captain, Borda made a number of contributions to Mathematical Physics, and also showed considerable talent in the improvement of scientific instruments. He is commemorated by a statue in his native town of Dax, near Bordeaux, and by a Borda Society.1
1
Part 2 of the present book omits any discussion of the history of the mathematical theory of proportional representation (the author’s view being that such a theory would be immensely difficult to obtain and that even today a serious beginning to it has scarcely been made). A historical account of the main theorizing on P.R. is given in chapter 9 of Hoag and Hallett (1926).
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Notes
For an account of his work and all that is known of his life, see Jean Mascart (1919). This book is excessively long and digressive, though in the present connection pp. 128-34 are valuable. A lively and penetrating estimate of his work, written by one who had known him, has been left by S. F. Lacroix (1800). See also Todhunter (1865: 432-4).
[The statue, which was not an authentic likeness, was destroyed by the Germans in World War II.]
Op. cit. pp. 31-4 and 657-65.
Op. cit. pp. 659-60.
Two slips in Borda’s arithmetic, op. cit. p. 663, confuse the appearance of his argument.
Op. cit. p. 665.
For an account in English of Condorcet’s life and thinking, though it excludes his thought on elections and Political Science, see Schapiro (1934). This book gives adequate bibliographical notes. See also the essay in Morley (1886: 163-255).
Referred to for the remainder of this chapter as Essai.
Cf. Montucla and Lalande (1802: tome III 421). Montucla and Lalande mention a work of the mathematician S. A. Lhuilier, Examen du mode d’élection proposé en février 1793 à la Convention nationale de France, et adopté à Génève (1794 in 8°). I have been unable to locate any copy of Lhuilier’s book. [Now reprinted as Lhuilier 1794 in McLean and Urken (1995: 151-95).]
Cf. Condorcet (1847-9: tome I ix-xxvii).
The more amusing of his exasperated remarks are to be found at pp. 441-2.
See, for example, Condorcet (1785: 119-20).
The number of ways of making an ordered selection of three things is 3! = 6.
His rejection of his previous theory is made particularly clear at Condorcet 1785: Ixv.
Nanson (1882: 229); McLean and Urken (1995: 349).
Condorcet (1785: 295-6, clxxvii-clxxix). To avoid confusion, in the example that follows we have replaced Condorcet’s symbols a,b and c by f, g and h.
Condorcet’s connection with the Academy had begun in 1769, but he was not present at this meeting.
We examined the minutes of the Academy for the years 1779-83, without finding any reference to the theory of elections.
Op. cit. p. 657.
Condorcet 1847-9: tome 1, iv, Mascart 1919: 95-6. [DB was wrong—see introduction.]
See Bell (1937) chapter 11; and for an unconventional view of his character, Pearson (1929).
‘Leçons de Mathématiques, données à l’lÉcole Normale en 1795’, which appeared in the Journal de l’lÉcole Polytechnique, tome II, septième et huitième cahiers (Paris, June 1812). This material was reproduced, with minor verbal alterations, in the Essai Philosophique sur les Probabilités, which, after appearing separately (1814), was made the introduction to the second edition of the Théorie Analytique des Probabilités (1814). It was also in the second edition of the Théorie Analytique that his mathematical theory of elections first appeared. The relevant passages in Laplace (1886) are to be found at pp. xc-xciv and 277-9.
Crofton (1885: vol. XIX, 780, § 43) and Todhunter (1865: 546-8).
Lacroix (1800: 37-8) and Mascart (1919: 130).
Lacroix (1800: 13 and 16) and Mascart (1919: 67).
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McLean, I., McMillan, A., Monroe, B.L. (1998). Borda, Condorcet and Laplace. In: McLean, I., McMillan, A., Monroe, B.L. (eds) The Theory of Committees and Elections by Duncan Black and Committee Decisions with Complementary Valuation by Duncan Black and R.A. Newing. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4860-3_18
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