CONDORCET, Marquis de. Essai sur l’Application de l’Analyse a la Probabilité des Décisions Rendues à la Pluralité des Voix.
Paris: Imprimerie Royale, 1785. First edition.

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 subject was one that departed from the natural sciences and mathematics but nevertheless showed the way toward a scientific comprehension of human phenomena, taking the empirical approach of natural science as its inspiration and employing mathematics as its tool. Condorcet called this new science "social mathematics". It was apparently 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, 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 judgment. Condorcet's entire analysis consisted, then, of calculating different variable functions of these structural 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 mutually independent. For example, the influence of a leader might intervene; or several successive 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 elementary 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 judgment in the relative ordering of several candidates." (DSB). In his analysis Condorcet described several now famous results, including Condorcet's jury theorem, his voting paradox, and the Condorcet election method. Scarce.

4to: 255 x 203 mm. Contemporary calf, rebacked. Some light browning to the last 20 pages. (2), CXCI, 304 pp.