Francis Ysidro Edgeworth on the regularity of law and the impartiality of chance
In 1925 Charles Percy Sanger did not hesitate in depicting his friend Francis Ysidro Edgeworth as a scientist who does not write treatises, but who could nevertheless influence the work of other scholars. In Edgeworth’s obituary in the Economic Journal, John Maynard Keynes (1926: 149) took a different view and suggested that the failure to venture on treatises was a contributory motive in the failure of Mathematical Psychics to fulfil its early promise. After eighty years, it is now clear that Keynes was wrong and Sanger was right in their estimate of Edgeworth’s contribution. In fact, it is even difficult to list all the scholars who credit Edgeworth of some path-breaking contributions in economics and statistics. As foreshadowed by Sanger, Edgeworth’s contributions have been absorbed in the common stock of knowledge as devices for modern microeconomics, contributing to the development of neoclassical economics. With the appearance of modern game theory, Edgeworth’s conjecture has acquired a new relevance as for example in Shubik (1959) and Scarf (1962). Ronald Coase (1988), in his ‘Note to the problem of social cost’, attributed to the unconscious reminiscences of Edgeworth’s Mathematical Psychics a substantial part in his famous theorem, as the basis of the modern economic analysis of law. Edgeworth’s contributions to the probabilistic foundation of statistics are now considered a substantial part of the ‘statistical revolution’ in the social sciences at the end of nineteenth century (Stigler 1978, 1986, 1999); and he is considered the precursor of many modern statistical devices, such as two-way analysis of variance, correlation coefficients, tests of significance and Edgeworth expansion. The fate invariably encountered by his contribution is to be rediscovered years later. This may be due to his idiosyncratic style and pattern of research and to the fact that his works appear fragmented and without a clear discernible path.
This fragmentation is evident from his bibliography which includes at least four books, 198 journal articles, 204 reviews and 139 entries for Palgrave (Baccini 2003). In fact a comprehensive reconstruction of Edgeworth’s works is still lacking in the literature; and the interested reader must refer to the partial stories offered by Creedy (1986), Newman (1987) and Mirowski (1994) for economics, Bowley (1928) and Stigler (1978, 1986, 1999) for statistics, Baccini for probability (1997, 2001, 2004) and ethics (2007). Nearly all scholars studying Edgeworth papers are puzzled by his pattern of research, especially in the years between 1878 and 1890, when he switched abruptly from ethics, to economics, to probability theory and finally to statistics. On one interpretation, these changes are attributable to external causes such as favourable or critical reviews or his personal search for a hero. On another interpretation, the changing pattern of interests can be explained as facets of his pursuit of a general scientific approach. This chapter takes the latter view and argues that the unitary approach of Edgeworth’s analysis can be grasped if attention is focused on the foundations of the various disciplines to which Edgeworth contributed and on the role played by probability theory. This procedure was also adopted by Mirowski (1994) but despite some common points, his reconstruction differs radically from the one presented here.