An axiomatic approach to intergenerational equity

We present a set of axioms in order to capture the concept of equity among an infinite number of generations. There are two ethical considerations: one is to treat every generation equally and the other is to respect distributive fairness among generations. We find two opposite results. In Theorem 1, we show that there exists a preference ordering satisfying anonymity, strong distributive fairness semiconvexity, and strong monotonicity. However, in Theorem 2, we show that there exists no binary relation satisfying anonymity, distributive fairness semiconvexity, and sup norm continuity. We also clarify logical relations between these axioms and non-dictatorship axioms. Received: 30 August 2000/Accepted: 18 March 2002 This paper is based on Chapt. 4 of my Masters Thesis [15] submitted to Kobe University, and won the Kanematsu Fellowship from the Research Institute for Economics and Business Administration of Kobe University in May 2001. I am grateful to Jun Iritani for helpful discussions and encouragement, two anonymous referees of this journal, three anonymous referees of the Kanematsu Fellowship, Eiichi Miyagawa, Noritsugu Nakanishi, Nguyen Huu Phuc, Hiroo Sasaki, Koji Shimomura, William Thomson, and Toyoaki Washida for detailed comments. I also thank participants at the spring meeting of Japanese Economic Association at Yokohama City University in May 2000, at the annual meeting of the Society for Environmental Economics and Policy Studies in Tsukuba in September 2000, and at the Kanematsu Fellowship Seminar at Kobe University in May 2001 for valuable comments.     

Anonymity and neutrality in Arrow’s Theorem with restricted coalition algebras

 In the very general setting of Armstrong (1980) for Arrow’s Theorem, I show two results. First, in an infinite society, Anonymity is inconsistent with Unanimity and Independence if and only if a domain for social welfare functions satisfies a modest condition of richness. While Arrow’s axioms can be satisfied, unequal treatment of individuals thus persists. Second, Neutrality is consistent with Unanimity (and Independence). However, there are both dictatorial and nondictatorial social welfare functions satisfying Unanimity and Independence but not Neutrality. In Armstrong’s setting, one can naturally view Neutrality as a stronger condition of informational simplicity than Independence. Received: 11 August 1994/Accepted: 1 April 1996     

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     

On the leximin and utilitarian overtaking criteria with extended anonymity

We present an extension of the overtaking criterion, called fixed-step overtaking social welfare relation (SWR), and its leximin counterpart, called fixed-step W-leximin SWR, for the evaluation of infinite utility streams. Our SWRs satisfy Fixed-step Anonymity. First, we characterize them by using the consistency, called Weak Fixed-step Indifference Consistency, which links indifference for infinite utility streams to indifference for their truncated vectors that are taken periodically. Second, we characterize another utilitarian extension, called S{\mathcal{S}}-overtaking SWR, by replacing the consistency with Fixed-step Anonymity. The S{\mathcal{S}}-overtaking SWR is a subrelation of the fixed-step overtaking SWR. Meanwhile, the leximin counterpart of the S{\mathcal{S}}-overtaking SWR coincides with the fixed-step W-leximin SWR, and we obtain its alternative characterization using Fixed-step Anonymity. Finally, we generalize the impossibility of combining Fixed-step Anonymity with the catching-up SWR by showing the Pareto and strong consistency axioms satisfied by the catching-up SWR come in conflict with Fixed-step Anonymity.     

Equitable Intergenerational Preferences on Restricted Domains

This paper examines the existence of equitable preferences on intergenerational consumption paths in an infinite horizon setting. There are two ethical considerations that capture the concept of intergenerational equity: inequality aversion in allocations and equality in treating generations. They are embodied in the Pigou–Dalton principle and anonymity, respectively. We investigate the existence of binary relations that satisfy these two axioms, as well as other standard axioms, such as monotonicity, transitivity, or continuity, on various domains. We show that any domain admitting such a binary relation is quite restricted: its interior is empty and contains no sustainable consumption path.     

Deservingness put into practice: Constructing the (un)deservingness of migrants in four European countries

The increased comparative research on perceptions of public welfare deservingness studies the extent to which different subgroups of citizens are deemed worthy or unworthy of receiving help from the welfare state. The concept of deservingness criteria plays a crucial role in this research, as it theorizes a universal heuristic that citizens apply to rank people in terms of their welfare deservingness. Due to the mainly quantitative nature of the research and despite the indisputable progress it has made, the subjective existence and actual application of these deservingness criteria remain a bit of a black box. What criteria of deservingness do citizens actually apply, and how do they apply them? This article opens the black box of welfare deservingness and sheds light on the nature and practice of deservingness criteria. Empirically, the paper explores how the deservingness of immigrants is discussed and established within 20 focus groups conducted in Slovenia, Denmark, UK, and Norway in 2016 with a total of 160 participants. All 20 focus groups discussed the welfare deservingness of immigrants based on similar vignette stimuli. Our analysis shows that (1) deservingness criteria are used both to construct images of target groups and as normative yardsticks; (2) deservingness criteria do not work independently of each other, but rather co-function in specific hybridized discourses; and (3) the moral logic of deservingness is supplemented by alternative moral logics, at least in the case of migrants.     

Freedom of choice in a social context: comparing game forms

In this paper, the set of outcomes of game forms is introduced as the relevant attribute for evaluating freedom of choice. These sets are defined as the cartesian product of every individual’s set of available options. It is argued that doing so is one way of taking into account social interactions when evaluating individual freedom. A set of axioms is introduced, each of which conveys some intuitions about how interactions affect freedom of choice, axioms by the mean of which two criteria, the Max and the MaxMin, are characterised for comparing game forms in terms of the freedom of choice they offer. These criteria are based, respectively, on the comparison of the best and the worst outcome the individual can reach in the game form.     

The measurement of structural and exchange income mobility

Chakravarty, Dutta and Weymark (1985) present operational axioms for an ethical index of income mobility that are best suited for a two period world. This paper suggests a decomposition of this index into two terms: (i) an index of structural or snapshot mobility, which captures the welfare effect of differences in the inequality of the cross-section income distributions; and (ii) an index of exchange or rerankings mobility, which captures the welfare impact of rank reversals between the first- and the second-period income distributions. Income inequality reductions and rank reversals are always welfare enhancing. The properties of all the income mobility concepts introduced in the paper do not require any new value judgements beyond the traditional ones.     

Reference functions and possibility theorems for cardinal social choice problems

 In this paper, we provide axiomatic foundations for social choice rules on a domain of convex and comprehensive social choice problems when agents have cardinal utility functions. We translate the axioms of three well known approaches in bargaining theory (Nash 1950; Kalai and Smorodinsky 1975; Kalai 1977) to the domain of social choice problems and provide an impossibility result for each. We then introduce the concept of a reference function which, for each social choice set, selects a point from which relative gains are measured. By restricting the invariance and comparison axioms so that they only apply to sets with the same reference point, we obtain characterizations of social choice rules that are natural analogues of the bargaining theory solutions. Received: 8 August 1994/Accepted: 12 February 1996     

Social aggregators

This paper proposes a general framework for analyzing a class of functions called social aggregators, which map profiles of linear orders to a set of binary relations. This class of aggregators includes aggregators that yield a preference relation (social welfare functions) and those which yield a choice of an alternative (social choice functions). Equipped with this framework, I identify a property called Preference Reversal (PR) such that any Pareto efficient aggregator having this property must be dictatorial. This allows me to state a general impossibility theorem, which includes Arrows Theorem and the Gibbard Satterthwaite Theorem as two special examples. Furthermore, I show that monotonicity and IIA are closely linked, by demonstrating that both are actually special cases of PR in specific environments.Received: 15 October 2001     

Mental Health Consumer and Carer Participation in Professional Education: ‘Getting There Together’ for Children of Parents with Mental Illness and Their Families

Abstract

‘Getting There Together’ is a professional education seminar developed as a collaborative project by professionals, mental health consumers and carers aimed at service providers who work with children of parents with mental illness and their families. The need for such professional education concerning this group is well recognised and the project reported herein was initiated by a reference group of professionals, consumers and carers focusing on children of parents with mental illness in the Eastern region of Melbourne (Victoria, Australia). The project began and continued as a collaborative effort during development and implementation, which ensured the experience, point of view and voice of consumers and carers was central to the material prepared, and at the time of seminar presentations. Seminar participants were from the family welfare, child care and supported housing sectors. Seminar participants found the first person accounts of consumers and carers the most helpful aspects of the seminars because they gave new insights into the experiences of carers and of mental health consumers as parents, as well as an understanding of ‘… the whole family, and how the child fits into the picture’.     

Multidimensional inequality and multidimensional generalized entropy measures: An axiomatic derivation

This paper generalizes the axiomatic approach to the design of income inequality measures to the multiattribute context. While the extension of most axioms considered desirable for inequality indices is straightforward, it is not entirely clear when a situation is more unequal than another when each person is characterised by a vector of attributes of well-being. We explore two majorization criteria which are partial orders ranking distributions of attributes by their degree of inequality. The two criteria are motivated by the Pigou-Dalton Transfer Principle in the unidimensional context and its equivalent formulation. These criteria gauge inequality loosely speaking with respect to the dispersion of the multidimensional distribution of the attributes. They, however, fail to address a different dimension of multivariate inequality pertaining to an increase in the correlation of the attributes. In this connection, this paper introduces a correlation-increasing majorization criterion proposed by Boland and Proschan (1988). Finally, in conjunction with other axioms commonly invoked in the literature on inequality, the majorization criteria lead inexorably to the class of multidimensional generalized entropy measures. Received: 15 June 1995 / Accepted: 30 September 1997     

Multi-profile intergenerational social choice

In an infinite-horizon setting, Ferejohn and Page showed that any social welfare function satisfying Arrow’s axioms and stationarity must be a dictatorship of the first generation. Packel strengthened this result by proving that no collective choice rule generating complete social preferences can satisfy unlimited domain, weak Pareto and stationarity. We prove that this impossibility survives under a domain restriction and without completeness. We propose an alternative stationarity axiom and show that a social welfare function on a specific domain satisfies this modified version and some standard social choice axioms if and only if it is a chronological dictatorship.     

Unemployment duration and the measurement of unemployment

We propose a framework in which the welfare bases of various unemployment measures available in the literature can be analyzed and a decomposition of these measures can be made into aggregate unemployment and the concentration of its distribution. A set of axioms for an unemployment measure is then introduced, which relate to the sensitivity of an unemployment measure to the inequality in the distribution of the unemployment. An unemployment measure is derived on the basis of these axioms that captures the distributional considerations in the measurement of unemployment.      

Appropriate discounting of future utilities need not be the dictatorship of the present: A note on Chichilnisky

Positive, but non-excessive discounting of future utilities to take account of possible non-realization/survival is not the dictatorship of the present, contrary to Chichilnisky's argument which is ingenious but contains a slip due to the improper treatment of infinity. As the probability of people existing a trillion to the power of a trillion years from now is close to zero, the fact that their voice now is also close to zero should not be regarded as the dictatorship of the present. Correspondingly, Chichilnisky's criterion which gives the welfare of people in year infinity some extra weight over-and-above their due weight in accordance to the realization probability, is not acceptable. This paper is drafted during my visit to the City University of Hong Kong late in 2001 and revised during my visit to the National University of Singapore in 2002. I am particularly grateful Professors Eden Yu and Euston Quah. The motivation for writing this paper is sparked by my drafting of the theme paper on welfare economics and sustainable development, published as Ng and Wills (2002), for UNESCO and EOLSS.     

A graphical analysis of some basic results in social choice

We use a simple graphical approach to represent Social Welfare Functions that satisfy Independence of Irrelevant Alternatives and Anonymity. This approach allows us to provide simple and illustrative proofs of May's Theorem, of variants of classic impossibility results, and of a recent result on the robustness of Majority Rule due to Maskin (1995). In each case, geometry provides new insights on the working and interplay of the axioms, and suggests new results including a new characterization of the entire class of Majority Rule SWFs, a strengthening of May's Theorem, and a new version of Maskin's Theorem. Received: 31 July 1999/Accepted: 27 March 2001     

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.     

Ranking opportunity sets: An approach based on the preference for flexibility

We describe a criterion to evaluate subsets of a finite set of alternatives which are considered as opportunity sets. The axioms for set comparison are motivated within the preference for flexibility framework. We assume the preference over the universal set of alternatives to be made of two disjoint binary relations. The result is the axiomatic characterization of a procedure which is formally similar to the leximax ordering, but in our case it incorporates the presence of some uncertainty about the decision-maker final tastes. Received: 20 January 1999/Accepted: 20 October 1999     

A non-dictatorial compromise

Abstract aggregations are defined and pertinent conditions of decisiveness, anonymity, unanimity, independence of irrelevant alternatives (stronger than the Arrowian) and non-dictatoriality (logically independent of the Arrowian) are developed for aggregations of choices. The mode is identified as a compromise aggregating variable societies of choices into a social choice, and it is shown (Theorem 4.1) to satisfy these conditions. This non-dictatorial compromise is then characterized (Theorem 5.1) in terms of three axioms paralleling those characterizing the approval voting of Sertel [7].This paper has benefited from helpful discussions with a number of colleagues and students, who are hereby thanked without being implicated for any remaining failings. In particular, earlier versions received the useful comments of participants at the Eighth and Ninth Bosphorus Workshops on Industrial Democracy, July 1983 and August 1984, Boaziçi University, Istanbul: most notably, Nick Baigent, Faruk Gül and Dennis Mueller. The help of Ünal Zenginobuz is also gratefully acknowledged. Finally, an anonymous referee's suggestions led to the addition of clarifying notes relating the notions of independence of irrelevant alternatives and of non-dictatoriality here to the usual Arrowian ones, and it is due to this referee's instigation that the characterization of the mode in Sect. 5 was produced.     

Characterizations of two power indices for voting games with r alternatives

In the first three sections of this paper we present a set of axioms which provide a characterization of an extension of the Banzhaf index to voting games with r alternatives, such as the United Nations Security Council where a nation can vote “yes”, “no”, or “abstain”. The fourth section presents a set of axioms which characterizes a power index based on winning sets instead of pivot sets. Received: 4 April 2000/Accepted: 30 April 2001