Ferdinando Galiani’s Newtonian Social Mathematics

The evolution of Ferdinando Galiani’s thought toward social mathematic has been neglected by scholars, and his attempt to establish political arguments on the analytical basis remains unexplored. The non-systematic nature of Galiani’s intuitions, due to his laziness, largely justifies this underestimation of his scientific program. This paper intends to show that the mature abbé Galiani follows an intellectual itinerary autonomous and parallel to that followed by Marquis de Condorcet in the same years. The anti-Physiocratique querelle represents Galiani’s methodological maturation. In contrast with Physiocratic economic doctrine, based on the primacy of deductive methodology, Galiani claims for economic science the realism of circumstance against aprioristic axiomatic hypotheses and rationalist generalizations. Galiani’s project, substantially similar to Marquis de Condorcet’s approach to social science, can be defined as Newtonian social mathematics opposed to Physiocratic Cartesian social mathematics.

A functional equation of tail-balance for continuous signals in the Condorcet Jury Theorem

Consider an odd-sized jury, which determines a majority verdict between two equiprobable states of Nature. If each juror independently receives a binary signal identifying the correct state with identical probability p, then the probability of a correct verdict tends to one as the jury size tends to infinity (Marquis de Condorcet in Essai sur l’application de l’analyse à la probabilité des décisions rendues à la pluralité des voix, Imprim. Royale, Paris, 1785). Recently, Alpern and Chen (Eur J Oper Res 258:1072–1081, 2017, Theory Decis 83:259–282, 2017) developed a model where jurors sequentially receive independent signals from an interval according to a distribution which depends on the state of Nature and on the juror’s “ability”, and vote sequentially. This paper shows that, to mimic Condorcet’s binary signal, such a distribution must satisfy a functional equation related to tail-balance, that is, to the ratio $$\alpha (t)$$ α ( t ) of the probability that a mean-zero random variable satisfies X$$>t$$ > t given that $$|X|>t$$ | X | > t . In particular, we show that under natural symmetry assumptions the tail-balances $$\alpha (t)$$ α ( t ) uniquely determine the signal distribution and so the distributions assumed in Alpern and Chen (Eur J Oper Res 258:1072–1081, 2017, Theory Decis 83:259–282, 2017) are uniquely determined for $$\alpha (t)$$ α ( t ) linear.

FERDINANDO GALIANI’S NEWTONIAN SOCIAL MATHEMATICS

The evolution of Ferdinando Galiani’s thought toward social mathematic has been neglected by scholars, and his attempt to establish political arguments on the analytical basis remains unexplored. The non-systematic nature of Galiani’s intuitions, due to his laziness, largely justifies this underestimation of his scientific program. This paper intends to show that the mature abbé Galiani follows an intellectual itinerary autonomous and parallel to that followed by Marquis de Condorcet in the same years. The anti-Physiocratique querelle represents Galiani’s methodological maturation. In contrast with Physiocratic economic doctrine, based on the primacy of deductive methodology, Galiani claims for economic science the realism of circumstance against aprioristic axiomatic hypotheses and rationalist generalizations. Galiani’s project, substantially similar to Marquis de Condorcet’s approach to social science, can be defined as Newtonian social mathematics opposed to Physiocratic Cartesian social mathematics.

Institution-Induced Stability

Simple majority rule is badly behaved. This is one of the earliest lessons learned by political scientists in the positive political theory tradition. Discovered and rediscovered by theorists over the centuries (including, famously, the Majorcan Franciscan monk Raymon Llull in the thirteenth century, the Marquis de Condorcet in the eighteenth, the Reverend Charles Dodgson (Lewis Carroll) in the eighteenth, and Duncan Black in the twentieth), the method of majority rule cannot be counted on to produce a rational collective choice. In many circumstances (made precise in the technical literature), it is very likely (a claim also made precise) that whatever choice is produced will suffer the property of not being “best” in the preferences of all majorities: for any candidate alternative, there will always exist another alternative that some majority prefers to it. This chapter suggests that while a collection of preferences often cannot provide a collectively “best” choice, institutional arrangements, which restrict comparisons of alternatives, may allow majority rule to function more smoothly. That is, where equilibrium induced by preferences alone may fail to exist, institutional structure may induce stability.

Public Choice

This chapter reviews the early contributions to public choice beginning with what might be called its antecedents. These include the works of the Marquis de Condorcet (1743–1794), Jean-Charles de Borda (1733–1799), Charles L. Dodgson (Lewis Carroll) (1823–1898), Harold Hotelling (1895–1973), Knut Wicksell (1851–1926), and Joseph A. Schumpeter (1883–1950). The chapter dates the modern literature from 1948, starting with the work of Duncan Black (1908–1991). It defines the early modern literature as spanning the twenty-five years after Black’s first contributions (1948–1973). The chapter proceeds by chronicling the contributions of the leading figures in public choice over that period in addition to Black—James M. Buchanan (1919–2013), Kenneth J. Arrow (1921–2017), Kenneth O. May (1915–1977), Anthony Downs (1930–), Gordon Tullock (1922–2014), William Vickrey (1914–1996), William H. Riker (1920–1993), Mancur Olson (1932–1998), James S. Coleman (1926–1995), Amartya K. Sen (1933–), and William A. Niskanen (1933–2011). It offers some final thoughts on the early literature in the closing section.

Wars of the Roses

During the latter half of the eighteenth century, opposition to the sexual theory intensified among social and religiously conservative asexualists who felt threatened by the political theories of the Enlightenment. For some, the Linnaean system was a stalking horse for libertinism, radical Jacobinism, feminism and anarchy. They maintained their ideological purity citing philosophical, religious and pedagogical reasons for rejection. Among the opponents were the Marquis de Condorcet, Hans Möller and William Smellie. Lazzaro Spallanzi and Charles Alston tried, but failed, to repeat Camerarius’s experiments. Flowers were so feminized symbolically the idea that most flowers were hermaphroditic seemed perverse, but Mary Wollstonecraft attacked hyper-feminine poetic metaphors for women as inimical to the struggle for equality. Meanwhile, hybridization experiments by Joseph Gottlieb Koelreuter eliminated the last rational objection to the sexual theory and demolished the preformationist theory, in both ovist and spermist versions. Christian Konrad Sprengel laid the foundation for floral ecology.