STABILIZATION POLICY: A RECONSIDERATION

Should stabilization policy be a macroeconomic priority? Most central banks consider it a goal, but Robert Lucas has contended that policies to stabilize output, even if effective, yield negligible welfare gains. This article critiques Lucas's argument. Existing literature suggests nontrivial benefits from stabilization due to nonlinearity of the social welfare function and of the short‐run Phillips curve. Our analysis and examination of the evidence from periods of prolonged high unemployment also suggest further significant gains to stabilization since the “accelerationist” hypothesis does not seem to hold in times of very low inflation. (JEL E61, E63)     

The measurement of opportunity inequality: a cardinality-based approach

We consider the problem of ranking distributions of opportunity sets on the basis of equality. First, conditional on a given ranking of individual opportunity sets, we define the notion of an equalizing transformation. Then, assuming that the opportunity sets are ranked according to the cardinality ordering, we formulate the analogues of the notions of the Lorenz partial ordering, equalizing (Dalton) transfers, and inequality averse social welfare functions – concepts which play a central role in the literature on income inequality. Our main result is a cardinality-based analogue of the fundamental theorem of inequality measurement: one distribution Lorenz dominates another if and only if the former can be obtained from the latter by a finite sequence of rank preserving equalizations, and if and only if the former is ranked higher than the latter by all inequality averse social welfare functions. In addition, we characterize the smallest monotonic and transitive extension of our cardinality-based Lorenz inequality ordering. Received: 2 May 1995 / Accepted: 11 October 1996     

An axiomatic characterization of the lexicographic maximin extension of an ordering over a set to the power set

The lexicographic maximin extension of an ordering is an important and widely used tool in social choice theory. We provide an axiomatization of it by means of five axioms. When the basic ordering is linear the following four (independent) axioms are sufficient: (1) Gärdenfors principle; (2) Neutrality; (3) Strong Fishburn monotonicity; and (4) Extension. Our result may also have applications in the theory of individual choice under uncertainty.     

Dictatorial domains in preference aggregation

We call a domain of preference orderings “dictatorial” if there exists no Arrovian (Pareto optimal, IIA and non-dictatorial) social welfare function defined over that domain. In a finite world of alternatives where indifferences are ruled out, we identify a condition which implies the dictatoriality of a domain. This condition, to which we refer as “being essentially saturated”, is fairly weak. In fact, independent of the number of alternatives, there exists an essentially saturated (hence dictatorial) domain which consists of precisely six orderings. Moreover, this domain exhibits the superdictatoriality property, i.e., every superdomain of it is also dictatorial. Thus, given m alternatives, the ratio of the size of a superdictatorial domain to the size of the full domain may be as small as 6/m!, converging to zero as m increases.     

Size and distribution trade-offs for the leximin ordering

A relative invariant and an absolute invariant inequality ordering satisfying extreme bottom-sensitivity, are proposed. It is shown that the leximin social welfare ordering can be expressed in terms of a ranking of distributions on the sole basis of their size, measured by the mean, and the degree of inequality, measured according to these inequality concepts. Leximin thus exhibits extreme bottom-sensitivity. This property does not withstand that leximin prefers a larger size of the cake at the cost of higher inequality in a number of cases. These trade-offs between size and equality are characterised in terms of degrees of dominance of the lower parts of the ordinary and absolute Lorenz curves that are accepted by leximin for a given increase in the mean.     

From Welfare to Work? Social Policy for Disabled People of Working Age in the United Kingdom in the 1990s

Disabled people of working age have been at the heart of recent welfare restructuring in the United Kingdom, but this has received little attention from mainstream social policy analysis. Both Conservative and Labour governments have introduced measures to promote labour force participation among disabled people, whilst discouraging dependence on welfare benefits. Whilst this new approach has been justified in terms of reducing poverty, its underlying imperatives are essentially inegalitarian. The welfare reform process has been driven by a number of official concerns including a perception of unsustainable fiscal pressures and a belief that perverse incentives in the social security benefit system have undermined economic efficiency. Moreover, it has been legitimated by an ideology of citizenship, which has shifted the moral responsibility for needs satisfaction away from the state to the individual. The paper concludes by identifying a better approach to welfare reform for disabled people of working age.     

THE WELFARE EFFECTS OF THIRD‐DEGREE PRICE DISCRIMINATION IN A DIFFERENTIATED OLIGOPOLY

This article examines the welfare effects of third‐degree price discrimination under oligopolistic competition with horizontal product differentiation. We derive a necessary and sufficient condition for price discrimination to improve social welfare: the degree of substitution must be sufficiently greater in the “strong” market (where the discriminatory price is higher than the uniform price) than in the “weak” market (where it is lower). It is verified, however, that consumer surplus is never improved; social welfare improves solely owing to an increase in the firms' profits in the case of linear demands. (JEL D43, L11, L13)     

The Lorenz zonotope and multivariate majorizations

 The distribution of d commodities among n individuals is described by an n×d row stochastic matrix. We present a geometric approach to order such matrices. For a row stochastic matrix the Lorenz zonotope is investigated, which is a higher dimensional generalization of the Lorenz curve. The Lorenz zonotope is a convex polytope. The inclusion of Lorenz zonotopes defines an ordering between row stochastic matrices, which is a multivariate majorization. For a cone in nonnegative d-space, a cone extension of the Lorenz zonotope and the respective inclusion ordering are introduced. We study this class of orderings and establish equivalence with known majorizations. It is provided a finite set of inequalities to which the ordering is equivalent. Received: 16 February 1994/Accepted: 22 May 1996     

Aggregation of coarse preferences

We consider weak preference orderings over a set A _n of n alternatives. An individual preference is of refinement?≤n if it first partitions A _n into ? subsets of `tied' alternatives, and then ranks these subsets within a linear ordering. When ?<n, preferences are coarse. It is shown that, if the refinement of preferences does not exceed ?, a super majority rule (within non-abstaining voters) with rate 1− 1/? is necessary and sufficient to rule out Condorcet cycles of any length. It is argued moreover how the coarser the individual preferences, (1) the smaller the rate of super majority necessary to rule out cycles `in probability'; (2) the more probable the pairwise comparisons of alternatives, for any given super majority rule. Received: 29 June 1999/Accepted: 25 February 2000     

Social work education in Cyprus: prospects and challenges in developing an indigenous character

The evolution of the social work education and welfare system in Cyprus is inextricably linked to the country’s recent turbulent history. Social Work in the Republic of Cyprus, although shaped by the country’s turbulent political past and present, is also influenced by Western theory as in many other countries in the Asian and African continent [Gray, M., & Fook, J. (2004). The quest for a universal social work: Some issues and implications, Social Work Education, 23(5), 625–644; Rankopo, M. J., & Hwedie, K. O. (2011). Globalization and culturally relevant social work: African perspectives on indigenization. International Social Work, 54(1), 137–147; Yip, K. S. (2007). Tensions and dilemmas of social work education in China. International Social Work, 50(1), 93–105]. In contrast with social welfare which has a long history (since late nineteenth century), social work education is still at an early stage of development in Cyprus. A non-surprising situation given that social work practice and education, in its early stages, is essentially a modernist Western invention which has a history of silencing marginal voices and importing, into diverse cultural contexts across the world, Western thinking primarily from the UK and the USA (Gray & Fook, 2004). However, if an indigenous social work character is to be developed in Cyprus, and a more distinctive identity with regard to the social work academic curricula is to be demonstrated, then Payne’s [(2001). Knowledge bases and knowledge biases in social work. Journal of Social Work, 1(2), 133–136] views on social work knowledge need further exploration.     

‘Non-interference’ implies equality

We propose a new principle of ‘non-interference’ applied to social welfare orderings. The principle, together with two other standard requirements, implies a strong egalitarian conclusion: the ordering must lexicographically maximize the welfare of the worst off. The first version of this paper was written when Mariotti was visiting Bocconi University. Their generous hospitality and financial support through a Research Fellowship is gratefully acknowledged. A previous version of this paper written by Mariotti alone was circulated with the title ‘Liberalism implies equality’. We thank Ken Binmore, Paola Manzini, Juan Moreno Ternero and two referees for helpful comments. The responsibility for any error is our own.     

Fairness,the veil of ignorance and social choice

A point of departure for this study is the recognition that various individuals may have different opinions about the exact form a social welfare function should have. To obtain some kind of amalgamation of differing individual social preferences, a modified version of the Rawlsian veil of ignorance is used and a definition of social efficiency suggested and analysed. A socially efficient state is defined by means of endogenous and individual veils of ignorance and, in addition, the Pareto principle. Efficiency may be described as a situation where individuals with similar social preferences constitute subsocieties in an optimal manner. Furthermore, a state is fair if it is (socially) efficient and equitable. An extension of the concept of fairness, called weak fairness, is also suggested. The analysis in this study does not presuppose any objective interpersonally comparable measure of utility.I would like to thank Professor Gevers, editor of this journal, and two anonymous referees for valuable comments on this paper. Support from the Swedish Council for Research in the Humanities and Tore Browaldh's foundation for Research and Education is gratefully acknowledged.     

Top-Pair and Top-Triple Monotonicity

We say that a social choice function (SCF) satisfies Top-k Monotonicity if the following holds. Suppose the outcome of the SCF at a preference profile is one of the top k-ranked alternatives for voter i. Let the set of these k alternatives be denoted by B. Suppose that i’s preference ordering changes in such a way that the set of first k-ranked alternatives remains the set B. Then the outcome at the new profile must belong to B. This definition of monotonicity arises naturally from considerations of set “improvements” and is weaker than the axioms of strong positive association and Maskin Monotonicity. Our main results are that if there are two voters then a SCF satisfies unanimity and Top-2 or Top-pair Monotonicity if and only if it is dictatorial. If there are more than two voters, then Top-pair Monotonicity must be replaced by Top-3 Monotonicity (or Top-triple Monotonicity) for the analogous result. Our results demonstrate that connection between dictatorship and “improvement” axioms is stronger than that suggested by the Muller–Satterthwaite result (Muller and Satterthwaite in J Econ Theory 14:412–418, 1977) and the Gibbard–Sattherthwaite theorem.     

Lexicographic measurement of the information contained in opportunity sets

An individual who has to choose one item from an opportunity set or menu may lack complete information about the final consequences attached to her choice. This problem has been modeled by Bossert (2000) who introduces an axiomatic approach to the ranking of menus according to their informational content. We propose a different ranking based on the lexicographic ordering on the vectors of numbers of consequences for each item and characterize it axiomatically. Received: 12 June 1998/Accepted: 5 September 2000     

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.     

Social choice with independent subgroup utility scales

In this article, the kinds of utility comparisons that can be made may differ in distinct population subgroups. Within each subgroup, utility is either ordinally or cardinally measurable. Levels and differences of utility may or may not be interpersonally comparable within a subgroup. No utility comparisons are possible between subgroups. Given these informational assumptions, it is shown that any continuous social welfare ordering that satisfies the weak Pareto principle only depends on the utilities of one of the subgroups. The class of social welfare orderings consistent with these assumptions is determined by the scale type of the dictatorial subgroup. Received: 25 May 1999/Accepted: 4 November 1999     

Symmetry extensions of “neutrality”

For n3 candidates, a system voting vector W ⁿ specifies the positional voting method assigned to each of the 2 ⁿ –(n+1) subsets of two or more candidates. While most system voting vectors need not admit any relationships among the election rankings; the ones that do are characterized here. The characterization is based on a particular geometric structure (an algebraic variety) that is described in detail and then used to define a partial ordering among system voting vectors. The impact of the partial ordering is that if W ⁿ ₁ W ⁿ ₂, then W ⁿ ₂ admits more kinds of (single profile) voting paradoxes than W ⁿ ₁. Therefore the partial ordering provides a powerful, computationally feasible way to compare system voting vectors. The basic ideas are illustrated with examples that completely describe the partial ordering for n=3 and n=4 candidates.This reearch was supported in part by NSF Grant IRI-9103180.     

Social welfare functions with a reference income

A foundation of social welfare functions is considered with a given reference income (or utility): relative and absolute invariance of the underlying welfare ordering are defined to hold for societies with either all members having incomes below the reference income or all members having incomes above the reference income. These conditions, alongside standard properties of a social preference relation, provide reference income dependent extensions of traditional classes of welfare functions. Dalton’s principle of positive transfers is incorporated, under which relative invariance leads to a class of piecewise (rank-)linear welfare functions, including the class of generalized Gini social welfare functions as a special case. To ensure quasi-concavity a new preference condition is proposed, which has the interpretation of aversion to income dropping below the reference income.     

On the Arrow and Wilson impossibility theorems

A social welfare function is Arrovian if it is transitive-valued and satisfies IIA. We examine the logical relation between the statements (A) If f is Arrovian with domain 𝒫 then it is dictatorial if it satisfies the Pareto criterion and (W) If f is Arrovian with domain 𝒫 then it is dictatorial or inversely dictatorial if it is non-null and satisfies non-imposition. We exhibit a class of domains on which W implies A and another on which A implies W. We also present examples of domains on which one of the statements is true and the other is false. Received: 23 October 2001/Accepted: 19 March 2002 We thank our two referees for their suggestions for improving the exposition.     

Unequivocal majority and Maskin-monotonicity

The unequivocal majority of a social choice rule is a number of agents such that whenever at least this many agents agree on the top alternative, then this alternative (and only this) is chosen. The smaller the unequivocal majority is, the closer it is to the standard (and accepted) majority concept. The question is how small can the unequivocal majority be and still permit the Nash-implementability of the social choice rule; i.e., its Maskin-monotonicity. We show that the smallest unequivocal majority compatible with Maskin-monotonicity is n- ë \fracn-1m û{n-\left\lfloor \frac{n-1}{m} \right\rfloor} , where n ≥ 3 is the number of agents and m ≥ 3 is the number of alternatives. This value is equal to the minimal number required for a majority to ensure the non-existence of cycles in pairwise comparisons. Our result has a twofold implication: (1) there is no Condorcet consistent social choice rule satisfying Maskin-monotonicity and (2) a social choice rule satisfies k-Condorcet consistency and Maskin-monotonicity if and only if k 3 n- ë \fracn-1m û{k\geq n-\left\lfloor \frac{n-1}{m}\right\rfloor}.