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When health is measured by a bounded variable, differences in health can be presented as levels of attainment or shortfall. Measurement of heath inequality then usually involves the choice of either the attainment or the shortfall distribution, and this choice may affect comparisons of inequality across populations. A number of indices have been introduced to overcome this problem. This chapter proposes a framework in which attainment and shortfall distributions can be jointly analyzed. Joint distributions of attainments and shortfalls are defined from points of view consistent with concerns for relative, absolute or intermediate inequality. Inequality measures invariant according to the corresponding ethical criterion are then applied. A dominance criterion that guarantees unanimous rankings of the joint distributions is also proposed.

In the unidimensional poverty field, a number of axioms capture the distribution sensitivity among the poor. One of them is the monotonicity sensitivity axiom that demands that a poverty measure should be more sensitive to a reduction in the income of a poor person, the poorer that person is. On the other hand, the minimal transfer axiom requires poverty to decrease when a transfer of income is made from a poor person to a poorer one. These axioms turn out to be identical, but they provide different and interesting interpretations. Both of them rely deeply on the income-ranking of the poor.

Some generalizations of the minimal transfer axiom and its variations have been proposed in the multidimensional framework. In none of them the partial ordering of the poor is taken into account. No counterpart of the monotonicity sensitivity axiom exists.

This note introduces multidimensional generalizations of the two mentioned axioms, keeping the crucial assumption that only when the poor involved are unambiguously ranked are the axioms uncontroversial. We show that the two generalizations proposed are also identical in the multidimensional setting although offering different interpretations. Relationships between the new properties and those existing in the literature are analyzed.

Purpose: Most of the characterizations of inequality or poverty indices assume some invariance condition, be that scale, translation, or intermediate, which imposes value judgments on the measurement. In the unidimensional approach, Zheng (2007a, 2007b) suggests replacing all these properties with the unit-consistency axiom, which requires that the inequality or poverty rankings, rather than their cardinal values, are not altered when income is measured in different monetary units. The aim of this paper is to introduce a multidimensional generalization of this axiom and characterize classes of multidimensional inequality and poverty measures that are unit consistent.

Design/methodology/approach: Zheng (2007a, 2007b) characterizes families of inequality and poverty measures that fulfil the unit-consistency axiom. Tsui (1999, 2002), in turn, derives families of the multidimensional relative inequality and poverty measures. Both of these contributions are the background taken to achieve our characterization results.

Findings: This paper merges these two generalizations to identify the canonical forms of all the multidimensional subgroup- and unit-consistent inequality and poverty measures. The inequality families we derive are generalizations of both the Zheng and Tsui inequality families. The poverty indices presented are generalizations of Tsui's relative poverty families as well as the families identified by Zheng.

Originality/value: The inequality and poverty families characterized in this paper are unit and subgroup consistent, both of them being appropriate requirements in empirical applications in which inequality or poverty in a population split into groups is measured. Then, in empirical applications, it makes sense to choose measures from the families we derive.

Purpose – A counting approach based on the number of deprivations suffered by the poor is quite an appropriate framework to measure multidimensional poverty with ordinal or categorical data. A method to identify the poor and a number of poverty indices have been proposed to take this framework into account. The implementation of this methodology involves the choice of a minimum number of deprivations required in order for an individual to be identified as poor. This cutoff and the choice of a poverty measure to aggregate the data are two sources of arbitrariness in poverty comparisons. The aim of this chapter is twofold. We first explore properties that characterize an identification method which allows different weights for different dimensions. Then the chapter examines dominance conditions in order to guarantee unanimous poverty rankings in a counting framework.

Design/methodology/approach – In the unidimensional poverty field, one branch of the literature is devoted to establishing dominance criteria that guarantee unanimous orderings at a variety of poverty thresholds and indices. This chapter takes this literature as a starting point, and investigates circumstances in which these ordering conditions may be applied in a weighted counting framework.

Findings – Necessary and sufficient conditions are obtained that guarantee that two vectors, which represent the weighted sum of the deprivations felt by each person, may be unanimously ranked regardless of the identification cutoff and of the poverty measure.

Originality/value – Since most of the data available for measuring capabilities or dimensions of poverty is either ordinal or categorical, the counting approach provides an alternative framework that suits these types of variables. The implementation of the ordering conditions derived in this chapter is based on simple graphical devices that we call dimension deprivation curves. These curves become a useful way to check the robustness of poverty rankings to changes in the identification cutoff. They also provide a tool for determining nonambiguous poverty rankings in a wide set of multidimensional poverty indices that suit ordinal and categorical data.

Volume 18 of Research on Economic Inequality contains selected papers from the Society for the Study of Economic Inequality's Third Annual Meeting (July, 2009) in Buenos Aires, Argentina. The volume collects eleven papers, five of which focus on inequality and poverty in Latin America. The Latin American papers address basic needs and poverty, multidimensional poverty, educational mobility, poverty dynamics, and the role of cash transfer programs in addressing inequality. The second half of Volume 18 collects other papers by ECINEQ members. The topics covered include taxation and inequality, evaluating poverty orderings, testing for mobility dominance, measuring relative deprivation, estimation of the costs of maintaining a child, and evaluating nutritional inequality.