Freedom of choice and diversity of options: Some difficulties

This paper explores the possibility for a (non-preference-based) freedom ranking of opportunity sets that is sensitive to the diversity of the options. It turns out that how distances between sets and alternatives are measured is crucial to the derivation of such a ranking. Several proposals are examined, each of which is shown to lead to impossibility results. Earlier versions of this paper were presented at conferences in Kortrijk, Osnabrück, Oisterwijk, Caen and Pavia. I thank the participants at these conferences for their comments. I would also like to thank Steven Hartkamp, Theo Kuipers, Clemens Puppe and especially Kotaro Suzumura for their helpful comments. Furthermore, I am very grateful to Somdeb Lahiri for pointing out a mistake in a previous version of this paper.     

Two families of rules for the adjudication of conflicting claims

We define two families of rules to adjudicate conflicting claims. The first family contains the constrained equal awards, constrained equal losses, Talmud, and minimal overlap rules. The second family, which also contains the first two of these rules, is obtained from the first family by exchanging, for each claims problem, how well agents with relatively larger claims are treated as compared to agents with relatively smaller claims. In each case, we identify the subfamily of consistent rules. I gratefully acknowledge support from NSF under grant SES-0214691. I also thank Tarık Kara, Cori Vilella, and in particular Juan Moreno-Ternero, Rodrigo Velez, and a referee, for their comments. This paper grew out of a section of the Condorcet Lecture I delivered at the VI-th International Meeting of the Social Choice and Welfare Society, Alicante, July 2000.     

Intergenerational preference orderings

This paper investigates preference orderings on infinite horizon intergenerational consumption streams. The trade-offs inherent in the selection of moral precepts for an intergenerational preference ordering are made explicit by establishing the mutual inconsistency of an appealing set of axioms.I am grateful to Don Campbell for many valuable discussions and comments. I have also benefitted from the comments of Mike Peters, participants in the Theory Workshop at the University of Toronto, and from a referee and editor of this journal.     

Utility and the individual: An analysis of internal conflicts

Herbert Simon has argued that economic agents do not maximise a transitive ordering but rather adopt what he calls satisficing behaviour. He argues that such behaviour is rational. This paper aims to provide a theory to support Simon's viewpoint. Because of social choice problems an individual with multiple objectives may find it impossible to construct a transitive ordering and hence may have to adopt satisficing type behaviour. We show that whether or not an individual adopts satisficing behaviour depends on the information available.I would like to thank Amartya Sen, the members of a seminar in Oxford, and an anonymous referee for their comments on previous drafts of this paper.     

Lives and well-being

This article attempts to use the analytical framework of social choice theory for exploring the ethical foundations of population policies. It is argued that non-existence is not a state and therefore that different numbers problems are conceptionally different from same numbers problems that concern much theoretical welfare economics. By means of examples it is argued that we should not expect to find an overall ethical ordering of social states when the size of future generations is subject to choice.This is a totally revised version of a paper (Dasgupta 1983) prepared for Professor Menahem Yaari's workshop on Social Choice Theory and Welfare Economics at the Hebrew University, Jerusalem, in the Spring of 1983. It was also presented at the meeting of the Working Group of the US National Academy of Science Committee on Population Growth and Economic Development held during August 2–4, 1984 at Woods Hole, Massachusetts. One strand of this earlier version, with extensions, was subsequently published in the volume of the Working Group: D. Gale Johnson and R. D. Lee (eds) (1987). I have benefitted greatly from discussions over the past several years with Kenneth Arrow, Robert Aumann, Simon Blackburn, Charles Blackorby, John Broome, David Donaldson, George Garnett, Peter Hammond, John Harsanyi, David Kelsey Marc Nerlove, Derek Parfit, John Rawls, Tim Scanlon, Paul Seabright, Amartya Sen, Robert Sugden, and Menahem Yaari. While preparing this eassay I received an extended letter from Jan Graaff in which he reflected on some of the issues discussed in the earlier paper.This present version bears the impact of his comments.     

Measuring and implementing equality of opportunity for income

Departing from the welfarist tradition, recent theories of justice focus on individual opportunities as the appropriate standard for distributive judgments. To explore how this philosophical conception can be translated into concrete public policy, we select the income as relevant outcome and the income tax as the relevant redistributive policy, and we address the following questions: (i) what is the degree of opportunity inequality in an income distribution? (ii) how to design an opportunity egalitarian income tax policy? Several criteria for ranking income distributions on the basis of equality of opportunities are derived. Moreover, we characterize an opportunity egalitarian income tax and we formulate criteria for choosing among alternative tax schedules. I would like to thank Peter Lambert for his encouragement and guidance, and Walter Bossert, Maurice Salles, and partecipants at the 1998 Social Choice and Welfare Conference, Vancouver, and at the Conference on Non–Welfaristic Issues in Normative Economics in Caen for their helpful comments and suggestions. Financial support of the Ministero dellIstruzione, Università e Ricerca (Italy) is gratefully acknowledged. Responsibility for any remaining deficiency is mine.     

Representing an ordering when the population varies

This note describes a domain of distributions of wellbeing, in which different distributions may have different populations. It proves a representation theorem for an ordering defined on this domain. Received: 19 September 2001/Accepted: 4 March 2002 I am extremely grateful to Sarah Moss for very helpful comments, and also to the journal's editor and referees. This note was written while I was a Visiting Fellow at the Research School of Social Sciences at the Australian National University.     

Measurement of inequality: An attempt at unification and generalization

This paper reviews and extends the theory of ethical inequality indices. It presents a novel axiom (strict separability of social welfare orderings in rank-ordered subspaces). This axiom allows to provide joint characterizations of the most important inequality measures (Atkinson family, Kolm-Pollak family and Generalized Ginis) and of some new more general classes of indices. The whole derivation is based on weak assumptions. In an ordinal framework only continuity of the underlying ordering is required and no cardinal properties are employed.I thank two anonymous referees for helpful comments and suggestions.     

Opportunity sets and individual well-being

 An opportunity set ranking rule assigns an ordering of opportunity sets to each individual utility function (defined on the universal set of alternatives) within the domain of this rule. Using an axiomatic approach, this paper characterizes a general class of opportunity set ranking rules which are based on the utilities associated with the elements of an opportunity set. It is argued that the addition of an alternative to a given opportunity set is not necessarily desirable in terms of overall well-being, and this position is reflected in replacing a commonly used monotonicity axiom with an alternative condition. Received: 15 May 1995/Accepted: 14 December 1995     

On ranking linear budget sets in terms of freedom of choice

This paper examines how freedom of choice as reflected in an agents opportunity sets can be measured in economic environments where opportunity sets are linear budget sets in the non-negative orthant of the n-dimensional real space. Three axioms, Symmetry, Monotonicity and Invariance of Scaling Effects, are proposed for this purpose and the measure based on volumes of budget sets is characterized. I am grateful to Prasanta K. Pattanaik for his encouragement and fruitful discussions over many years on this and related subjects. The first draft of this paper was written while I was visiting the Institute of Economic Research at Hitotsubashi University in Japan. I would like to thank its hospitality. Helpful comments of a referee are gratefully acknowledged.     

Optimal sequential decision architectures and the robustness of hierarchies and polyarchies

This paper studies collective decision making in the context of a project selection model. We derive the optimal decision architecture in the presence of marginal decision costs, and investigate the circumstances under which the hierarchy and polyarchy emerge as optimal sequential architectures. Our analysis extends previous results on optimal organizational decision-making to a sequential setting, and further demonstrates the fragility of the hierarchy and polyarchy as optimal architectures.I would like to thank Ruth Ben-Yashar, Thorbjorn Knudsen, Shmuel Nitzan, Raaj Sah and Peter Norman Sorensen for comments on earlier versions of the paper. I have also benefited greatly from the advice and suggestions of two anonymous referees and the Coordinating Editor, Maurice Salles. The results in this paper were presented at the Economic Architecture Conference, 21–22 June 2003, at Odense, Denmark. I would like to thank the University of Southern Denmark and the Danish Social Science Research Council for their hospitality, and the participants at the Workshop for their constructive comments. Research support from the Singapore Management University is also gratefully acknowledged. The usual disclaimer applies here.     

Recoverability of choice functions and binary relations: some duality results

Banerjee and Pattanaik (1996) proved a theorem that the maximal set with respect to a quasi-ordering can be fully recovered by defining the greatest sets with respect to each and every ordering extension thereof and taking their union. Donaldson and Weymark (1998) proved a theorem that a quasi-ordering can be fully recovered by taking the intersection of all the ordering extensions thereof. These recoverability theorems are obviously related, but their exact relationship has never been clarified in the literature. This paper examines the issue of choice-functional recoverability and relational recoverability in a general framework, and establishes several remarkable duality relationships. Thanks are due to Professors Walter Bossert, Prasanta K. Pattanaik, Clemens Puppe, Amartya K. Sen, and John Weymark, with whom we had several opportunities to discuss this and related issues. The first author also would like to express his gratitude to the Andrew Young School of Policy Studies, Georgia State University, and the Scientific Research Grant for Policy Areas (B) Number 603 from the Ministry of Education, Science and Culture of Japan for their financial support which made this collaborative research possible. We are also grateful to the referees whose comments have led to several improvements of the paper.     

On the equivalence between welfarism and equality of opportunity

A welfarist way of allocating resources consists in 1) equipping individuals with comparable indices of their well-being and 2) applying a unique aggregation rule to individual well-being levels. An equality of opportunity way of allocating resources consists in 1) making the distinction between personal characteristics which are under and beyond individuals control, and 2) decreasing inequalities due to differences in characteristics beyond individuals control. We show that under the proviso that indifferent individuals should not influence social judgements, welfarist and equal opportunity judgements on resource allocation are equivalent.This paper presents research results of the Belgian Program on Interuniversity Poles of Attraction initiated by the Belgian State, Prime Ministers Office, Science Policy Programming. I thank seminar participants at the Institute for Advanced Study and especially Eric Maskin for their comments, Louis Gevers and Yves Sprumont for stimulating discussions, and Walter Bossert, Marc Fleurbaey and two anonymous referees for detailed remarks and suggestions.     

THE FISCAL FRAMEWORK OF MONETARY POLICY

This paper i11ustrates the importance of the fiscal framework for monetary analysis by discussing three separate issues. I begin by examining how the fiscal framework changes the macroeconomic equilibrium associated with different steady state rates of money growth. This includes a summary of research that I have presented elsewhere and comments on several additional aspects of the way in which the fiscal structure destroys the neutrality of monetary policy.
The second section deals with the short-run impact of changes in monetary policy. Here again the fiscal structure complicates the economy's response to monetary policy.
The final section looks at the effect of the fiscal structure on the central banks choice of monetary policies. Fiscal structures are likely to influence the policies adopted because they affect the costs and benefits of monetary policies.     

Social welfare rankings of income distributions A new parametric concept of intermediate inequality

This paper installs a new concept of intermediate inequality, which we refer to as η-inequality equivalence, in the notable form of equivalence of the Lorenz partial ordering and social welfare dominance. The η-inequality equivalence is a parameterized generalization of Krtscha’s (1994) non-linear compromise between the relative and absolute inequality views. For each η ∈ [0,1], we place a class of social evaluation functions satisfying the S-concavity as well as the property that an increase in incomes while leaving η-inequality intact raises welfare. We prove that one income distribution dominates another for all social evaluation functions in iff the former has a higher mean and a higher η-Lorenz curve. We prove also that the class is strictly increasing in the sense of inclusion as η decreases.I am grateful to Kiyoshi Kuga for his helpful comments and suggestions. I am also grateful to an anonymous referee and an associate editor for many valuable comments and suggestions that have much improved the paper. A previous version of this paper was presented at the annual meeting of the Japanese Economic Association, October 7, 2001, Tokyo, Japan. I wish to thank Takashi Toyoda for his helpful comments and suggestions at the meeting. This research was supported in part by the Ministry of Education, Culture, Sports, Science and Technology in Japan (Grant-in-aid for Scientific Research No.12630032).     

Strategic behaviour and a notion of ex ante efficiency in a voting model

A person is said to prefer in the stochastic dominance sense one lottery-over-outcomes over another lottery-over-outcomes if the probability of his (at least) first choice being selected in the first lottery is greater than or equal to the analogous probability in the second lottery, the probability of his at least second choice being selected in the first lottery is greater than or equal to the analogous probability in the second lottery, and so on, with at least one strict inequality. This (partial) preference relation is used to define straightforwardness of a social choice function that maps profiles of ordinal preferences into lotteries over outcomes. Given a prior probability distribution on profiles this partial preference ordering (taking into account the additional randomness) is used to induce a partial preference ordering over social choice functions for each individual. These are used in turn to define ex ante Pareto undominated (efficient) social choice functions. The main result is that it is impossible for a social choice function to be both ex ante efficient and straightforward. We also extend the result to cardinal preferences and expected utility evaluations.This work was supported by Grant #SOC 77-27403 and #SES 80-26086 from the National Science Foundation. It has been prepared at the University of Illinois and the University of Pennsylvania. We want to thank Steve Matthews and an anonymous referee for helpful comments     

The illegal alien work force,demand for unskilled labor,and the minimum wage

Estimates of the illegal alien work force, employment, and the number employed below the legal minimum wage are not available, but are often required for the study of a variety of public policy issues, e.g., immigration and refugee policy, and policy towards the monitoring of minimum wage laws. This paper attempts to fill this void by developing estimates of these quantities. Of equal importance, however, is determining what light this and other related evidence throws upon the oft-expressed view that the demand for unskilled labor at below-legal-minimum wage rates is virtually inelastic. Evidence is presented which contradicts this belief. I am grateful to Janet Hunt and Richard H. Timberlake, Jr. for valuable comments but I absolve them of responsibility for any errors.     

Arrow’s Axiom and Full Rationality for Fuzzy Choice Functions

A classical result for crisp choice functions shows the equivalence between Arrow axiom and the property of full rationality. In this paper we study a fuzzy form of Arrow axiom formulated in terms of the subsethood degree and of the degree of equality (of fuzzy sets). We prove that a fuzzy choice function satisfies Fuzzy Arrow Axiom if and only if it is (fuzzy) full rational. We also show that these conditions are also equivalent with weak and strong fuzzy congruence axioms WFCA and SFCA. It is studied the Arrow index, a new concept that indicates the degree to which a fuzzy choice function satisfies the Fuzzy Arrow Axiom. The author wishes to express her gratitude to the two anonymous reviewers for their valuable comments and discussions that contributed to a higher quality of the paper. Some of their comments can be found in the final version of the paper. An abstract of this paper was presented at the First Spain Italy Netherlands Meeting on Game Theory SING, Maastricht, The Netherlands, June 2005.     

The ignorant observer

We propose an extension of Harsanyi’s Impartial Observer Theorem based on the representation of ignorance as the set of all possible probability distributions over individuals. We obtain a characterization of the observer’s preferences that, under our most restrictive conditions, is a convex combination of Harsanyi’s utilitarian and Rawls’ egalitarian criteria. This representation is ethically meaningful, in the sense that individuals’ utilities are cardinally measurable and fully comparable. This allows us to conclude that the impartiality requirement cannot be used to decide between Rawls’ and Harsanyi’s positions. We thank D. Bouyssou, A. Chateauneuf, M. Cohen, M. Fleurbaey, E. Karni, J.-F. Laslier, P. Mongin, J. Moreno-Ternero and especially J. Weymark, as well as seminar audiences at University Pompeu Fabra, University of Cergy-Pontoise, the Roy Seminar and RUD 2006 for useful comments. Comments by two anonymous referees have been extremely useful to improve the paper. Financial support from an ACI grant by the French Ministry of Research is gratefully acknowledged.     

Condorcet's jury theorem in light of de Finetti's theorem

This paper generalizes Condorcet's jury theorem to the case of symmetrically dependent votes with the help of de Finetti's theorem. Thus, the paper relaxes Condorcet's assumption of independent voting while preserving his main result: In jury-type situations a majority of voters is more likely than any single voter to choose the better of two alternatives.I am indebted to Professors Steven Brams, Arnold Buss, Gary Miller and Norman Schofield for their comments and questions. This paper is supported, in part, by a grant from the National Science Foundation (SES-9210800).