CONDORCET, MARIE-JEAN-ANTOINE-NICOLAS DE CARITAT DE. - ["SOCIAL MATHEMATICS"]
Essai sur l'application de l'analyse à la probabilité des décisions rendues à la pluralité des voix.
Paris, Imprimerie Royale 1785. 4to. (255x197mm). Beautiful contemporary full calf with five raised bands and elaborate spine gilding. Some light brown spotting to first and last leaves - otherwise clean throughout. An excellent copy of a very scarce work. (2),CXCI,(1),304 pp.
¶ First and only edition of the first large-scale attempt to apply mathematics to knowledge of human phenomena. "Condorcet's most significant and fruitful endeavor was in a field entirely new at the time The subjects was one that departed from the natural sciences and mathematics but nevertheless showed the way toward a scientific comprehnsion of human phenomena, taking the emperical approach of natural science as its inspiration and employing mathematics as its tool. Condorcet called this new science "social mathematics". It was apparantly intended to comprise, ..., a statistical description of society, a theory of political economy inspired by the Physiocrats, and a combinatorial theory of intellectual processes. The great work on the voting process, published in 1785 [the offered item], is related to the later. Condorcet there sought to construct a scheme for an electoral body the purpose of which would be to determine the truth about a given subject by the process of voting and in which each elector would have the same chance of voicing the truth. Such a scheme was presented exactly like what is today called a model. Its parameters were the number of voters, the majority required, and the probability that any particular vote voices a correct judgement. Condorcet's entire analysis consisted, then, of calculating different variable functions of these structual parameters. Such, for example, was the probability that a decision reached by majority vote might be correct. An interesting complication of the model is introduced by the assumption that individual votes are not mutuallyindependent. For example, the influence of a leadermight intervene; or several succesive polls are taken, the electors' opinions may change during the voting process. On the other hand, the problem of estimating the various parameters on a statistical basis was brought out by Condorcet, whose treatment foreshadowed very closely that employed by modern users of mathematical models in the social sciences. The mathematical apparatus may be reduced to simple theorems of addition and multiplication of probabilities, to binomial distribution, and to the Bayes-Laplace rule. ... Along the way he encountered a completely different problem, the decomposition and composition of electoral decisions in the form of elementary propositions on which voters pronounce either "Yes" or "No". He then anticipated, without being aware of it, the logical import of this problem, which was the theory of the sixteen binary sentence connectives among which he emphasized the conditional. He showed that a complex questionnaire could be reduced to a sequence of dichotomies and that constraints implicitly contained in the complex questionnaire are equivalent to rejection of certain combinations of "Yes" and "No" in the elemetary propositions. This is literally the reduction into normal disjunctive forms as practiced by contemporary logicians. He therefore brought to light, more completely and more systematically than his predecessor Borda, the possible incoherence of collective judgement in the relative ordering of several candidates." (Dictionary of Scientific Biography, vol. 3, pp.386-87). In his analysis Condorcet described several now famous results, including Condorcet's jury theorem, his voiting paradox, and the Condorcet election method.
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