Harsanyi's Aggregation Theorem: multi-profile version and unsettled questions

Harsanyi's Aggregation Theorem states that if the individuals' as well as the moral observer's utility functions are von Neumann-Morgenstern, and a Pareto condition holds, then the latter function is affine in terms of the former. Sen and others have objected to Harsanyi's use of this result as an argument for utilitarianism. The present article proves an analogue of the Aggregation Theorem within the multi-profile formalism of social welfare functionals. This restatement and two closely related results provide a framework in which the theorem can be compared with well-known characterisations of utilitarianism, and its ethical significance can be better appreciated. While several interpretative questions remain unsettled, it is argued that at least one major objection among those raised by Sen has been answered.The author is grateful to V. Barham, J. Broome, M. Fleurbaey, D. Hausman, S. Kolm, J. Roemer, and P. Suppes, for useful discussions and suggestions. Special thanks are due to C. d'Aspremont, N. McClennen, J. Weymark, and an anonymous referee for detailed comments on an earlier version. The usual caveat applies. The author also gratefully acknowledges financial support from the SPES programme of the Union Européenne.     

Capabilities and achievements: An empirical study

This paper contributes to the development of the capabilities approach by showing that capabilities can, counter prevailing wisdom, be measured. By operationalising the capabilities element of Sen's non-welfarist theory, the paper develops the data required by this novel approach to welfare economics and by exploring relations to life-satisfaction (happiness) it also examines new economic co-variates of experienced utility. A postal questionnaire is designed to examine elements of Sen's theory of capabilities and implemented on a random sample of English voters. Analysis of survey results includes ordinal logistic regression models of overall capabilities, rank correlations between own capabilities and views about the distribution of capabilities, rank correlations between capabilities and achievements and a set of ordered logit models explaining achievements as a function of corresponding capabilities. Furthermore, results show that it is possible to make statistically significant distinctions between different capabilities, that perceptions of others’ capabilities are sometimes related to own capabilities and that achievements appear, in general, to be related to corresponding capabilities. Finally, and in keeping with oft-found paradoxes in the happiness literature, an examination of co-variates suggests that satisfaction with capabilities might be negatively related to objective measures of opportunity.     

ANDREAS HEINRICH VOIGT AND THE HICKS‐ALLEN REVOLUTION IN CONSUMER THEORY

In 1893, Andreas Heinrich Voigt argued that utility admits only an ordinal characterization. We discuss the apparent impact of Voigt's now forgotten early argument for an ordinal approach to utility on later economists. Edgeworth cited Voigt's ordinal‐cardinal distinction several times in the Economic Journal, bringing both the concept and the terminology into Anglophone economics. In 1927, Rosenstein‐Rodan, too, cited Voigt's argument for ordinal utility. Since Hicks apparently learned the cardinal‐ordinal terminology from Edgeworth, and discussed utility theory and complementarity with Rosenstein‐Rodan, it appears that Voigt's 1893 article is the original source of ordinal utility in economics. (JEL B13, B21)     

Bergson social welfare functions in applied welfare analysis

Characterizations of the orderings induced on a set of alternatives by often-used Bergson Social Welfare Functions are provided. The characterizations are particularly useful in applied welfare analysis, because they are formulated entirely in terms of orderings of alternatives, rather than orderings of utilities, as is typically done.Helpful comments from Charles Blackorby, Ake Blomqvist, John Broome, Sam Bucovetsky, Mike Hoy, Glenn MacDonal, John Weymark and three referees are gratefully acknowledged, but the usual disclaimer applies.     

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.     

Bayesian utilitarianism and probability homogeneity

This paper investigates, within the axiomatic framework of Jeffrey-Bolker decision theory, two kinds of conditions and the relation between them: (1) The Utilitarian condition that social rankings of prospects be representable by an expected utility function that is a weighted sum of the expected utility functions representing individual rankings; and (2) Homogeneity conditions on the probabilities and preferences of individuals. In particular, we show that identity of individuals’ probabilities is necessary and sufficient for the Utilitarian condition to hold and that the homogeneity of individuals’ probabilities can be derived from a Pareto condition on the relation between individual and social rankings, provided that these rankings are separable in a particular sense.This paper has considerably benefited from comments by John Broome, Isaac Levi and an anonymous referee. Special thanks to Philippe Mongin who provided encouragement, help and careful criticism throughout the development of this paper.     

On the nature of Suppes–Sen maximal paths in an aggregative growth model

This article investigates the nature of paths in the standard neoclassical aggregative model of economic growth that are maximal according to the Suppes–Sen grading principle. This is accomplished by relating such paths to paths which are utilitarian maximal when an increasing (but not necessarily concave) utility function evaluates each period’s consumption. Dynamic properties of Suppes–Sen maximal paths, which lie entirely above or entirely below the golden-rule, are analyzed. An example is presented in which an explicit form of a consumption function is described, which generates only Suppes–Sen maximal paths. This consumption function is shown to generate consumption cycles, and violate the Pigou–Dalton transfer principle.     

Anonymous Single-profile Welfarism

This note reexamines the single-profile approach to social-choice theory. If an alternative is interpreted as a social state of affairs or a history of the world, it can be argued that a multi-profile approach is inappropriate because the information profile is determined by the set of alternatives. However, single-profile approaches are criticized because of the limitations they impose on the possibility of formulating properties such as anonymity. We suggest an alternative definition of anonymity that applies in a single-profile setting and characterize anonymous single-profile welfarism under a richness assumption.The paper was presented at the conference on welfarist and non-welfarist approaches to public economics in Ghent, March 2004. We thank John Broome, Campbell Brown, Marc Fleurbaey, Wlodek Rabinowicz, John Roemer, John Weymark and two referees for comments and discussions. Financial support through a grant from the Social Sciences and Humanities Research Council of Canada is gratefully acknowledged.     

To be or not to be involved: a questionnaire-experimental view on Harsanyi’s utilitarian ethics

According to standard theory founded on Harsanyi (J Polit Econ 61:434–435, 1953; 63:309–321, 1955) a social welfare function can be appropriately based on the individual’s approach to choice under uncertainty. We investigate how people really do rank distributions in terms of welfare. According to Harsanyi, the evaluation can be done from the standpoint of an uninvolved external judge, a public official, for example, or by a person who knows that she holds one of the positions in society, with an equal chance for any of the available positions. Are these two structures to be viewed differently? We use a questionnaire experiment to focus on the two different interpretations of the Harsanyi approach. There are important, systematic differences that transcend the cultural background of respondents.     

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.     

Governing Women's Capabilities in China's Urban Expansion

By the middle of the twenty-first century, China's urban population is likely to have grown by about 500 million, to more than 1.1 billion people. This article applies Amartya Sen's concept of capabilities to explore how the government of urban expansion is affecting the generation of rural women whose villages currently are being enclosed by cities and towns. Drawing on interviews, press reports and government and Women's Federation documents from Zhejiang province, it illustrates how local governments' economic growth strategies hinge, in part, on reconstructing gendered relations in the spatial organization, civic management, production and social reproduction in new metropolitan sites. The article concludes, first, that unless China's leaders commit to involving rural women's representatives in urban planning and management, enforcing women's rights to property and enabling women to decide whether and when to work and retire, the capabilities of this generation of rural women will expand little; and, second, that Sen's concept overlooks organizational and material conditions that are necessary for women to enhance their capabilities.     

On intra- and interpersonal utility comparisons

In this paper, it is suggested to formulate assumptions on the comparability of individual utilities in terms of meaningful statements rather than using the usual way of defining such assumptions by means of certain sets of admissible transformations. Various assumptions involving intra- and interpersonal comparisons of utility levels and utility differences are introduced in terms of meaningful statements and compared to their traditional counterparts. It is shown that these two approaches are, in general, not equivalent. In a social choice framework, it is demonstrated that the difference between these approaches can be quite substantial: replacing the usual cardinal unit comparability assumption by a condition involving comparisons of utility differences which is similar in spirit turns a well-known characterization of the utilitarian social welfare functional into an impossibility theorem.I am indebted to Charles Blackorby, David Donaldson, Michel Le Breton, and John Weymark for very helpful discussions and comments on an earlier version of the paper. The suggestions of two anonymous referees enabled me to improve the paper considerably.     

Normative population theory

Utilitarian and contractarian solutions to the problem of optimal population are examined and shown to have unacceptable implications. As argued by Parfit, for instance, utilitarianism may imply large numbers of people at a very low standard of living. An analogy is drawn between optimal population for a society and the optimal structure of an individual life. The ideal life need not maximize cardinal utility, because an individual may prefer a shorter life with less, more intense utility to a very long life with higher total utility (Methuselah's Paradox). The optimal population is what an individual would prefer if he had to sequentially live out each life in his choice.The author wishes to thank John Broome, Amihai Glazer, Jack High, Joseph Kalt, Randy Kroszner, Thomas Schelling and an editor of this journal for useful comments. The usual disclaimer applies.     

Adult-equivalence scales and the economic implementation of interpersonal comparisons of well-being

Equivalence Scale Exactness (ESE) or Independence of Base (IB), a condition on household preferences and interpersonal comparisons, makes adult-equivalence scales independent of utility levels. ESE is characterized by Income-Ratio Comparability (IRC) which assumes that utility equality is preserved by income scaling. If ESE/IRC is a maintained hypothesis, equivalence scales can be estimated from behaviour alone if preferences are not piglog. This condition is not met by a family of translog expenditure functions or by the Almost Ideal Demand System. A translog expenditure function can be used for the reference household, however, together with an independent specification of the equivalence scale.Earlier versions of this paper [1987–1992] have been presented at Amsterdam, Augsburg, Barcelona, Bilbao, CORE, Essex, GREQE, Kiel, Leyden, Madrid, Southhampton, Toulouse, UBC, and Valencia. We thank the seminar participants and the referees of this journal, and are especially indebted to Kenneth Arrow, Martin Browning, Dale Jorgenson, Joseph Ostroy, Shelley Phipps, J. Ruiz-Castillo, Daniel Slesnick, Terry Wales and John Weymark. We also thank Amartya Sen whose remarks on another paper inspired the approach we have taken in this one.     

Utility, informed preference, or happiness: Following Harsanyi's argument to its logical conclusion

Harsanyi (1997) argues that, for normative issues, informed preferences should be used, instead of actual preferences or happiness (or welfare). Following his argument allowing him to move from actual to informed preferences to its logical conclusion forces us to use happiness instead. Where informed preferences differ from happiness due to a pure concern for the welfare of others, using the former involves multiple counting. This “concerning effect” (non-affective altruism) differs from and could be on top of the “minding effect” (affective altruism) of being happy seeing or helping others to be happy. The concerning/minding effect should be excluded/included in social decision. Non-affective altruism is shown to exist in a compelling hypothetical example. Just as actual preferences should be discounted due to the effects of ignorance and spurious preferences, informed preferences should also be discounted due to some inborn or acquired tendencies to be irrational, such as placing insufficient weights on the welfare of the future, maximizing our biological fitness instead of our welfare. Harsanyi's old result on utilitarianism is however defended against criticisms in the last decade. Harsanyi (1997) argues, among other things, that in welfare economics and ethics, what are important are people's informed preferences, rather than either their actual preferences (as emphasized by modern economists) or their happiness (as emphasized by early utilitarians). The main purpose of this paper is to argue that, pursuing Harsanyi's argument that allows him to move from actual to informed preferences to its logical conclusion forces us to happiness as the ultimately important thing. The early utilitarians were right after all! Since I personally approve of Harsanyi's basic argument, I regard myself as his follower who becomes more Catholic than the Pope. (It is not denied that, in practice, the practical difficulties and undesirable side-effects of the procedure of using happiness instead of preferences have to be taken into account. Thus, even if we ultimately wish to maximize the aggregate happiness of people, it may be best in practice to maximize their aggregate preferences in most instances. This important consideration will be largely ignored in this paper.) The secondary objective is to give a brief defence of Harsanyi's (1953, 1955) much earlier argument for utilitarianism (social welfare as a sum of individual utilities) that has received some criticisms in the last decade. The argument (e.g. Roemer 1996) that Harsanyi's result is irrelevant to utilitarianism is based on the point that the VNM (von Neumann-Morgenstern) utility is unrelated to the subjective and interpersonally comparable cardinal utility needed for a social welfare function. Harsanyi's position is defended by showing that the two types of utility are the same (apart from an indeterminate zero point for the former that is irrelevant for utilitarianism concerning the same set of people). Received: 29 May 1997 / Accepted: 3 November 1997     

More on Harsanyi's utilitarian cardinal welfare theorem

If individuals and society both obey the expected utility hypothesis and social alternatives are uncertain, then the social utility must be a linear combination of the individual utilities, provided the society is indifferent when all its members are. This result was first proven by Harsanyi [4] who made implicit assumptions in the proof not actually needed for the result (see [5]). This note presents a straightforward proof of Harsanyi's theorem based on a separating hyperplane argument.I wish to thank Stephen Selinger for pointing out Resnick's argument to me and W. A. J. Luxemburg for a useful discussion which simplified the argument     

Twofold optimality of the relative utilitarian bargaining solution

Given a bargaining problem, the relative utilitarian (RU) solution maximizes the sum total of the bargainer’s utilities, after having first renormalized each utility function to range from zero to one. We show that RU is “optimal” in two very different senses. First, RU is the maximal element (over the set of all bargaining solutions) under any partial ordering which satisfies certain axioms of fairness and consistency; this result is closely analogous to the result of Segal (J Polit Econ 108(3):569–589, 2000). Second, RU offers each person the maximum expected utility amongst all rescaling-invariant solutions, when it is applied to a random sequence of future bargaining problems generated using a certain class of distributions; this is recalls the results of Harsanyi (J Polit Econ 61:434–435, 1953) and Karni (Econometrica 66(6):1405–1415, 1998).     

Non-expected utility maximizers behave as if expected utility maximizers: An experimental test

We investigate the behaviors of subjects who either do or do not adhere to the expected utility theory using the Becker–DeGroot–Marschak (BDM) method. We directly examine the validity of the expected utility theory in order to distinguish subjects into two groups: those who adhere to the expected utility theory (expected utility maximizers) and those who do not adhere to it (non-expected utility maximizers), and then execute the BDM experiment in the both groups. We find that the differences in the stated prices between the expected and non-expected utility maximizers are not significant. This result implies practical usefulness for the BDM method.     

Rethinking the European countryside—can we learn from the South?

A new paradigm of multi-dimensional rural development has emerged which advocates a broader conception of the rurality where the rural is no longer the monopoly of the farmer. This new, broader paradigm needs to be reflected in the methodology of social scientific research, both generic and applied. In this paper we are primarily concerned with transfer of research methodologies utilised in development studies in the South to explore their usefulness for rethinking the European countryside. Such a transfer of methodology may be helpful, because integrated rural development can build on a long legacy in the South, while it has only recently been advocated in the EU context. The paper reflects upon the application of two such analytical concepts originating from development studies, which we have applied for research on the rural geographies in the European countryside, namely Sen's livelihood capabilities approach and Chambers’ concept of participatory rural appraisal (PRA). Having the sustainable livelihoods approach as overall framework, both methodologies are qualitative in nature and address people's survival strategies and livelihood practices with a focus on micro-level analysis at individual, household (Sen) and community level (PRA), while reflecting their embeddedness in wider social, political and economic structures. Our comparative studies suggest that the prospects for bottom-up development, as orchestrated by PRA or similar approaches, is constrained by structural factors, which define the boundaries for local development. The capabilities approach is useful to detect the capabilities to act and be within which bottom-up approaches may take their—though limited—role in rural development.     

Taxpayer attitudes toward tax audit risk

Theoretical analyses on tax evasion usually assume that the taxpayer's behavior conforms to the Von Neumann-Morgenstern axioms for behavior under uncertainty, namely that the taxpayer is generally risk averse. This study found that the taxpayers' attitudes toward risk could be affected by (1) whether taxpayers perceive a tax payment as reduced income or as a loss; and (2) the magnitude of the tax savings and penalty structure. The findings, in general, agree more with the prospect theory than with the classical expected utility theory.