Mathematical Psychics Research Articles

The Seligman-Edgeworth Debate about the Analysis of Tax Incidence: The Advent of Mathematical Economics, 1892-1910

This debate took place over eighteen years in a series of publications that I shall chronicle below, starting with Edwin Robert Anderson Seligman's On the Shifting and Incidence of Taxation (SIT) in 1892, and ending sometime after 1910 with the appearance of Francis Ysidro Edgeworth's Applications of Probabilities to Economics in the Economic Journal (Seligman 1892; Edgeworth [1910] 1925). (1) Seligman's arguments are presented in each of the five successive editions of his master work (SIT) that were published during his lifetime. By the third edition, published in 1910, Seligman's arguments had reached something of a final mature form. Edgeworth took an early interest in the application of mathematics to social science questions, especially the blossoming theory of (Mirowski 1994: 30-47). In 1881, Edgeworth published his Mathematical Psychics, in which he remarkably extended utilitarian ethical theory in mathematical form and pioneered the analysis of exchange equilibrium in directions that have had an enormous influence on our modern understanding of equilibrium (Edgeworth [1881] 1995; Creedy 1998). In the first years of his appointment (1891) to the Drummond chair at All Souls College, Oxford, he engaged Seligman in matters that at first glance seem to have mostly to do with taxation theory. Edgeworth's responses to Seligman appeared primarily in the Economic Journal, which he edited from 1891 until shortly before his death in 1926. His last response to Seligman appeared in the Economic Journal in 1910 and most curiously invoked his favorite principle of unverified probability from his ongoing statistical studies to put the fledgling mathematical method--as he understood it--on a more secure ground in economics (Edgeworth [1910] 1925). This debate and its methodological significance have been mentioned by Harold Hotelling (1932) and discussed by John Creedy (1986, 1998), but their importance to our understanding of the application of mathematical analysis to economics in the twentieth century has been overlooked. The purpose of this article is to emphasize this aspect of the tax incidence debate. The arguments between these two protagonists were something like a tennis match: Seligman would make a statement in his book (SIT) and Edgeworth would publish his response with lightning speed in the form of a full-length article in the Economic Journal. Seligman would subsequently take notice of Edgeworth's arguments in time for the next revised edition of his great book, provoking Edgeworth to prepare another hasty reply to be published in the Economic Journal. On one level they debated a tiny and specialized issue in price theory--tax incidence theory. Indeed, this is the only way the debate has come down to us in the secondary literature. (2) On another level they debated the precise form economic analysis would assume throughout the greater part of the twentieth century. I am concerned here with both the substance of the taxation debate as well as the significance of the argument for the development of mathematical economics. Edgeworth had definite ideas on mathematical economics that were extreme, uncompromising, and at times dogmatic. He bitterly complained about Seligman's use of contrived numerical examples in economics to illustrate points of far-reaching principle. The modern calculus could not bear the weight of Seligman's blasphemous numerical examples. Seligman held his ground, quite undisturbed by Edgeworth's onslaughts. His obstinacy on this issue angered Edgeworth, who, in the end, appealed to a jury of both social scientists and natural scientists to come to his aid in his battle to slay the stubborn Seligman dragon. His principle of unverified probability was transposed from statistical analysis to economics to try to rule out certain functional forms and admit only smooth differentiable functions into economic arguments. Edgeworth's approach was the harbinger of what became the established approach of all textbook writers in the twentieth century, making economic ideas easily subject to mathematical analysis regardless of whether the changes involved are large or small. …

Sidgwick and Edgeworth on indeterminacy in the labour market

Commentators have underlined Sidgwick's influence on Edgeworth's thinking and more particularly on New and Old Methods of Ethics (1877). But have failed to notice that Sidgwick remained a major reference in Mathematical Psychics (1881). Therefore, the purpose of this paper is to show that, in this book, Edgeworth wanted to refine upon the problem of wages addressed by Sidgwick in 1879. The thesis of the paper is that Sidgwick and Edgeworth's disagreement as to the role of open competition in the resolution of indeterminacy in the labour market stems from two different notions of competition. This latter can be seen as a differentiation process, as in Sidgwick's, or as a replication mechanism, as in Edgeworth's.

A Pioneering Analysis of the Core: Turgot's Essay on Value

SECTION IThe idea of the core of an economy and the convergence of core allocations to the competitive equilibrium are well established in the economic literature. It has been assumed by most authors on this topic that it was Edgeworth who in his Mathematics Psychics first stated and proved the major result concerning the core. [Debreu and Scarf (1963), Arrow and Hahn (1971)]. The purpose of this paper is to draw attention to an essay by Turgot where the idea of the core is clearly stated and an argument about the convergence of the core to the competitive equilibrium as the number of consumers increases is first presented. Edgeworth’s Mathematical Psychics came out in 1881, Turgor’s essay was written some time in the 1760’s, definitely by 1770, but did not appear until Du Pont published his Oeuvres in 1808. Either way, if we can persuasively argue Turgot's claim then the discovery of this result is pushed back by more than a hundred years.

Efficient sets, decision heuristics, and single-peaked preferences

The origins of single-peaked preferences in multiattribute choice behavior are analyzed. The starting point is Coombs and Avrunin's ( Psychological Review, 1977, 84, 216–230; Journal of Mathematical Psychology, 1977 , 16, 261–266) theory which explains single-peakedness as the joint effect of task and behavior characteristics. Whereas the task conditions—so-called efficient sets—are retained, and their importance is even more stressed, it is argued that Coombs and Avrunin's behavioral assumptions—classical marginally decreasing preference functions—may not be representative of actually displayed choice behavior. Rather, the information processing approach to decision research has shown that multiattribute choices are often based on simplifying heuristic rules which, due to their possible intransitivity, are inconsistent with Coombs and Avrunin's behavioral requirements. Tversky's ( Psychological Review, 1969 , 76, 31–48) additive difference model is used as an algebraic framework for analyzing such so-called attribute-based choice rules. Sufficient (and in the continuous case also necessary) conditions are presented which guarantee that the additive difference model will also be single-peaked on efficient sets. These conditions show that the behavioral principles yielding single-peaked preferences are far more general than Coombs and Avrunin assumed and include most of the empirically substantiated forms of attribute-based choice rules. Further, a necessary and sufficient condition is derived which insures that elimination rules, like the conjunctive rule, for instance, and generalizations thereof are single-peaked. Finally, making use of a result by Edgeworth, ( Mathematical Psychics, London, Paul, 1881 ), it is shown that efficient sets per se may originate in quite different ways. It is concluded that the phenomenon of single-peakedness is mainly a function of the task rather than of some specific behavior.

Some Recent Interpretations of Mathematical Psychics: a Reply

Research Article| June 01 1980 Some Recent Interpretations of Mathematical Psychics: a Reply Vincent J. Tarascio Vincent J. Tarascio Search for other works by this author on: This Site Google History of Political Economy (1980) 12 (2): 277–281. https://doi.org/10.1215/00182702-12-2-277 Cite Icon Cite Share Icon Share Facebook Twitter LinkedIn MailTo Permissions Search Site Citation Vincent J. Tarascio; Some Recent Interpretations of Mathematical Psychics: a Reply. History of Political Economy 1 June 1980; 12 (2): 277–281. doi: https://doi.org/10.1215/00182702-12-2-277 Download citation file: Zotero Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search Books & JournalsAll JournalsHistory of Political Economy Search Advanced Search The text of this article is only available as a PDF. Copyright © 1980 by Duke University Press1980 Article PDF first page preview Close Modal Issue Section: Articles You do not currently have access to this content.

UTILITY THEORIES IN FIELD PHYSICS AND MATHEMATICAL ECONOMICS (I)

A NEW and more explicit approach to Field Theory was commenced by Francis Ysidro Edgeworth in 1881. His Mathematical Psychics was a conscious attempt to formulate the Field Analogy with respect to Utility Theory. 'The conception of a man as a pleasure-machine may justify and facilitate the employment of mechanical terms and mathematical reasoning in social science. Edgeworth was attracted by the problem of many bodies in dynamics and by the calculus of variations.2 (Walras' mathematical orientation was towards sectors of the classical calculus.) Edgeworth admired Lagrange, Hamilton, and Maxwell3 who, with the aid of their 'generalised co-ordinates' solved the great problems of maxima. He recognised a magnificent analogy to the human tendency to ' accumulate pleasure under existing conditions'. He devised his model of indifference maps on the pattern of fields of forces and established the fundamental analogy for conditions of equilibrium. 'The direction in which X will prefer to move, the line of force or line of preference, as it may be termed, is perpendicular to the line of indifference.'4 (The mathematical and geometrical parallelisms inherent in this statement were not formalised by Edgewortl.) The most significant advance, consciously drawn by Edgeworth from Field Theory, was his formulation of Utility as a function with several independent variables. Utility depends upon the combination of commodities in one's possession just as the potential function depends on the configurations of all co-ordinates. In 1871, ten years prior to Edgeworth, Stanley Jevons 5 already formulated economics as the ' calculus of pleasure and pain '. The' Hedonimetry' of Edgeworth opened a more accomplished phase in the progress of

Mathematical Psychics. An Essay on the Application of Mathematics to the Moral Sciences.

Mathematical Psychics. An Essay on the Application of Mathematics to the Moral Sciences.

The Mathematical Method in Political Economy

THE usefulness of mathematical reasoning applied to political economy, the value of the methods originated by Cournot and developed by Jevons, may be said to be still sub judice. The consideration of Messrs. Auspitz and Lieben's diagrams and symbols tends to confirm the opinion that mathematical analysis is a potent, if not an indispensable, means of obtaining clear general ideas in economics. The metaphysician who twists and turns the terms force and energy without I grasping their mathematical signification is not more likely to become entangled in his talk than the practical man who reasons about supply and demand, and cost and value, without having once for all considered the ideas in their clearest and most abstract form. For the purpose of this contemplation Messrs Auspitz and Lieben employ a construction differing from most of their predecessors; namely, a figure in which the abscissa represents the quantity of a certain commodity, the ordinate the amount of some other article—in particular, money—which is exchanged for that which the abscissa represents. We cannot, however, quite admit the statement: “Unsere Kurven unterscheiden sich schon durch die zu Grunde gelegten Koordinaten von Jenen unserer Vorgänger.” The same construction is used in the papers of an eminent English Professor, which, though unpublished, have been widely circulated in the learned world. It has also appeared in at least one English publication, Mr. Edgeworth's “Mathematical Psychics,” with due acknowledgment to the distinguished originator. Untersuchungen über die Theorie des Preises. Von Rudolf Auspitz Richard Lieben. (Liepzig: Verlag von Duncker und Humblot, 1889.)