Distributive Justice and Inequality: A Selection of Papers Given at a Conference, Berlin, May 1986 PDF
Preview Distributive Justice and Inequality: A Selection of Papers Given at a Conference, Berlin, May 1986
W. Gaertner P. K. Pattanaik (Eds.) Distributive Justice and Inequality A Selection of Papers Given at a Conference Berlin, May 1986 With 15 Figures and 6 Tables Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Prof. Dr. Wulf Gaertner Universitat Osnabriick Fachbereich Wirtschaftswissenschaften Postfach 4469 D-4500 Osnabriick, FRG Prof. Dr. Prasanta K. Pattanaik Department of Economics Faculty of Commerce and Social Science The University of Birmingham P.O. Box 363 Birmingham B 15 2IT, UK First published in "Social Choice and Welfare", Vol. 5, No.2 and 3, 1988. ISBN-13: 978-3-642-73818-0 e-ISBN-13: 978-3-642-73816-6 DOl: 10.1007/978-3-642-73816-6 Library of Congress Cataloging-in-Publication Data. Distributive justice and inequality IW. Gaertner, P. Pattanaik (eds.). p. cm. Papers presented at a conference on distributive justice and inequality, held at the Institute for Advanced Study Berlin, 5/20-24/1986. 1. Income distribution-Congresses. 2. Distributive justice-Congresses. I. Gaertner, Wulf. II. Pattanaik, Prasanta K. HB523.D57 1988 323.4'6-dc19 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. Duplication of this publication or parts thereof is only permitted under the provisions of the German Copyright Law of September 9,1965, in its version of June 24,1985, and a copyright fee must always be paid. ' Violations fall under the prosecution act of the German Copyright Law, © Springer-Verlag Berlin Heidelberg 1988 Softcover reprint of the hardcover 1 st edition 1988 The use of registered names, trademarks, etc, in the publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use, Preface From May 20 to May 24, 1986 a conference on distributive justice and in equality was held at the Institute for Advanced Study Berlin (Wis senschaftskolleg zu Berlin). More than thirty scholars participated in this conference. The topics of the presentations ranged from ethics, welfare economics and social choice theory to characterizations of inequality meas ures and redistributive taxation schemes. This book contains a selection of the papers given at the conference. This collection of articles also appeared as issues 2 and 3 of volume 5 of Social Choice and Welfare. In the first paper P. Suppes argues for a pluralistic concept of equity. For too long the emphasis has been on income distribution but there are other characteristics which are important when one talks about equity. Suppes suggests that it would be desirable to have Lorenz curves for a variety of fea tures of societies, such as education, health and housing. P. Dasgupta studies the quality of lives in terms of an index of living stand ards. One has to distinguish between "same number choices" (the number of lives is given) and "different numbers choices" (problem of optimum popUlation). The author argues that in the latter case the anonymity (or sym metry) axiom cannot be readily defended. Once it is dropped, however, an incoherence in the moral ordering of possible worlds arises. The moral basis for different numbers choices becomes generation-dependent, an overall moral ordering of possible worlds no longer exists. P. Hammond's contribution also concerns different numbers choices. Classical utilitarianism entails Parfit's "repugnant conclusion". Parfit drew attention to the fact that according to classical utilitarianism population must increase until the marginal individual's utility reaches zero, implying that it is better to have many people whose lives are barely worth living than having fewer more prosperous people. Hammond argues for parenting rights in order to avoid the repugnant conclusion. Parents' rights concerning the birth consequences of their children should be recognized. The next two papers present axiomatic characterizations of inequality measures. U. Ebert starts by characterizing social welfare orderings and then deduces inequality orderings from them. Ebert introduces a novel axiom re quiring independence with respect to ranked income vectors. A nice conse quence of this property is that joint characterizations of the most important inequality measures (the Atkinson and Kolm-Pollak families, the generalized Gini-coefficients) are possible. Ebert considers fixed and vari able population sizes. The class of inequality measures which W. Eichhorn examines, contains, as special cases, the measures which reflect the concept of relative inequality and those which reflect the concept of absolute inequal ity. The intermediate concepts analyzed by Eichhorn are characterized by the fact that multiples of convex combinations of proportional and absolute variations in all incomes leave inequality unaffected. VI J. Foster and A. Shorrocks examine the headcount ratio, the per-capita in come gap and a distribution sensitive measure in the context of discrete dis tributions. The authors establish logical relationships between the poverty orderings derived from the three indices and general types of welfare func tions which need not be additively separable with respect to individual in comes. The poverty ordering deduced from the headcount ratio, for exam ple, is logically equivalent to a welfare ordering which is based on a symmet ric and monotonic welfare function. The main objective of N. Kakwani's contribution is to explore how wel fare, income inequality and poverty change during the course of an under developed country's economic development. The author investigates whether Kuznets' hypothesis of an "inverted U-shaped pattern of income inequality" can be substantiated for Sri Lanka. There does not seem to exist a clear-cut result. Most of the inequality measures which were used show the inverted U-shaped pattern of development; there are, however, major differences as to when the turning point occurs. The degree of inequality aversion in the different measures of inequality plays a role here. The next three papers discuss distributional implications of alternative tax ation schemes. W. Buchholz, W. Richter and J. Schwaiger look at the princi ples of equal absolute sacrifice and equal proportional sacrifice. They prove that if distributional comparisons are based on income after a poll tax in stead of income before tax, assuming constant total revenue, equal propor tional sacrifice yields more equally distributed income than equal absolute sacrifice which, in its turn, leads to more equally distributed income than a poll tax. The emphasis in P. Moyes' contribution is on absolute rather than relative income inequality. Moyes formulates necessary and sufficient condi tions for a taxation scheme to be uniformly equalizing according to absolute Lorenz dominance. These conditions require that the taxation scheme be both incentive preserving and minimally progressive, properties which were introduced by Fei. A. Pfingsten presents a parametric class of inequality con cepts and derives, for each element of this class, a necessary and sufficient condition for taxation to be inequality-reducing. The relative and the abso lute view of inequality are just two members of the class of inequality con cepts considered by Pfingsten. For example, the result of Moyes which we have discussed earlier, can be recovered within the general framework of Pfingsten. Finally, T. Lensberg and W. Thomson start from an alternative characteri zation of the Nash bargaining solution, recently proposed by Lensberg. The objective of their paper is to find out the role which Pareto-optimality plays in this characterization of Lensberg (an analogous investigation was done, some time ago, by Roth with respect to Nash's original axiom system). The authors show that the only additional solution made possible through an abandonment of the Pareto condition is the solution which selects the origin as a solution outcome. It is a great pleasure to express our gratitude to all those who have so generously helped us in preparing this volume. We wish to thank all con tributors to this volume as well as the numerous referees for their friendly VII co-operation. We are greatly indebted to Deutsche Forschungsgemeinschaft for its generous support of the Berlin conference, and to the director and the staff of the Wissenschaftskolleg zu Berlin for their hospitality and assistance during the conference. Our special thanks go to SPRINGER-Verlag for making this volume possible. Wulf Gaertner Prasanta K. Pattanaik Contents Lorenz Curves for Various Processes: A Pluralistic Approach to Equity P.Suppes . 1 Lives and Well-Being P. Dasgupta . 15 Consequentialist Demographic Norms and Parenting Rights P. J. Hammond . 39 Measurement of Inequality: An Attempt at Unification and Generalization U. Ebert . 59 On a Class of Inequality Measures W. Eichhorn . 83 Poverty Orderings and Welfare Dominance J. E. Foster, A. F. Shorrocks . 91 Income Inequality, Welfare and Poverty in a Developing Economy with Applications to Sri Lanka N. Kakwani . 111 Distributional Implications of Equal Sacrifice Rules W. Buchholz, W. F. Richter, J. Schwaiger 135 A Note on Minimally Progressive Taxation and Absolute Income Inequality P. Moyes . 139 Progressive Taxation and Redistributive Taxation: Different Labels for the Same Product? A. Pfingsten . 147 Characterizing the Nash Bargaining Solution without Pareto-Optimality T. Lensberg, W. Thomson 159 Lorenz Curves for Various Processes: A Pluralistic Approach to Equity P. Suppes Department of Philosophy, Stanford University, Stanford, CA 94305, USA Abstract. Theoretical Lorenz curves for a bureaucracy with n seniority levels and similar curves for a simple stochastic economy with capitalistic opportunity to move up or down are derived. In both cases it is argued that equality of distribution is not an appropriate ideal. But the main thrust is that income alone is not a sufficient 'criterion of equity. A more general Aristotelian viewpoint is argued for. The marked increase in the equity of education between 1940 and 1984 in the United States is taken as a good example. But even within education, it is argued, detailed policies will realistically satisfy no simple set of equity principles. The appeal of principles that lead to an equal distribution of income is matched by the appeal of similar principles in the theory of belief. In the latter case, the result is a uniform probability distribution as the appropriate prior distribution. Several of the main principles used to defend a uniform distribution of value have also been used to defend the uniform distribution of belief, or conversely. The most salient example is the use of the principle of insufficient reason to justify a uniform distribution in either case. The Bayesian attack on a central principle of uniformity of belief has had a powerful impact. Classical or logical theories of probability that have attempted to justify the uniform distribution of belief as the only natural prior distribution are not currently well received. Of course, in real problems a uniform prior distribution has never had the role it was presumed to have in introductory discussions of the classical theory of probability. Perhaps the finest example is to be found in Laplace's classical treatise on probability. He announces that probajJility is to be defined in terms of the ratio of favorable cases to possible cases, but then this definition scarcely enters into any of the complex developments or applications he pursues. The Bayesian approach to belief is, in fact, suggestive of the proper approach to matters of equity. It is a mistake to think only in terms of simple first principles that justify egalitarianism. We need to think harder and in a more subtle way about the principles that justify various inequalities that are unlikely to be eliminated, or that, 2 P. Suppes in fact, most people would not want to see eliminated. Some examples are discussed in the first section. There is a second introductory point to be made about the viewpoint I advocate here. Too much discussion of matters of justice and equity has centered on unrealistic ideas such as those of Rawls concerning the initial distribution under the veil of ignorance, or, to take a quite different example, Nozick's idealized and equally unrealistic concept of entitlement. As in the case of Bayesian theories of belief, we are always in the middle of rebuilding the equity ship at sea. We are not going to run ourselves aground and start afresh. What actually dominates political considerations in debates about issues of equity is what we should do next, what direction we should go. It seems to me that what we need from a normative standpoint, therefore, is more analysis oflong-run outcomes, rather than analysis of inevitably dim beginnings. For this reason, I have concentrated in Sect. 2 on asymptotic Lorenz curves of distribution, but I recognize that these too should be taken with a grain of salt. We are not really interested in asymptotic results but always in much shorter-range results, as reflected in actual data in Sect. 4. The reason to discuss asymptotic results is just that it is easy to summarize the results of processes when we look at the asymptotic behavior. It may well be that the right normative consideration - right in the sense of proper modesty - is to think not at all in terms of asymptotic results but only in terms of direction of change. Such an analysis could be given for the processes discussed in Sect. 2, without much modification, and I do present in Sect. 4 some empirical results in this direction with respect to the distribution of education in the United States. In the first section I review briefly some earlier results of mine [6] concerned with seniority and income distribution in bureaucracies. The results might be described, perhaps facetiously, as socialism with class. In any case, I want to use the resulting Lorenz curves, and the corresponding Gini coefficients, to compare with various dynamic processes that could be put in place in the part of an economy that is market-driven. (Note that I deliberately do not say "in a market economy" because it seems to me we shall be faced forever with mixed economies, and in discussion of appropriate normative questions about distribution of income we must deal both with market forces and also with bureaucratic institutions.) The Gini coefficient can certainly be criticized as an appropriate single measure, but I use it here for simple comparative purposes. The analysis of inequality ordinarily centers around the Lorenz curve for income distribution. There is broad agreement on using the Lorenz curve to represent the distribution of income or wealth, but there is much less agreement over how to define a single measure of inequality to be derived from the Lorenz curve. The classical and most widely used measure is the Gini coefficient, which is used in Sects. 1 and 2. Sections 3 and 4 are concerned with the philosophical foundations of a pluralistic approach to equity. A broadly Aristotelian viewpoint is argued for, and one distribution example from education is worked out in detail. The final section moves to the microanalysis of equity. A second example from education concerned with allocation of instructional resources is to show concretely the practical impossibility of reaching agreement about determinant principles of equity at the micro level.
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