Ana Urrutia

Unit Consistency and Bipolarization of Income Distributions

Most of the polarization measures proposed in the literature, and likewise the inequality and poverty indices, assume some invariance condition, be that scale, translation or intermediate, which imposes value judgements on the measurement. In the inequality and poverty fields, B. Zheng suggests rejecting these invariance conditions as axioms and proposes replacing them with the unit-consistency axiom (Economica 2007, Economic Theory 2007 and Social Choice and Welfare 2007). This property demands that the inequality or poverty rankings, rather than their cardinal values, are not altered when income is measured in different monetary units. Following Zheng’s proposal we explore the consequences of the unit-consistency axiom in the polarization field and propose and characterize a class of intermediate polarization orderings which is unit-consistent.

A class of poverty measures induced by the dual decomposition of aggregation functions

In this paper we introduce a new family of poverty measures for comparing and ordering social situations. The aggregation scheme of these poverty measures is based on the one-parameter family of exponential means. The poverty measures introduced satisfy interesting properties and the dual decomposition of the underlying exponential means induces a natural decomposition of the proposed poverty indices themselves into three underlying factors: incidence, intensity, and inequality among the poor.

Characterizing multidimensional inequality measures which fulfil the Pigou-Dalton bundle principle

The Pigou–Dalton bundle dominance introduced by Fleurbaey and Trannoy (Social Choice and Welfare, 2003) captures the basic idea of the Pigou–Dalton transfer principle, demanding that, in the multidimensional context also, “a transfer from a richer person to a poorer one decreases inequality”. However, up to now, this principle has not been incorporated to derive multidimensional inequality measures. The aim of this article is to characterize measures which fulfil this property, and to identify sub-families of indices from a normative approach. The families we derive share their functional forms with others having already been obtained in the literature, the major difference being the restrictions upon the parameters.

A New Multiplicative Decomposition for the Foster–Greer–Thorbecke Poverty Indices

This paper identifies a multiplicative decomposition for the Foster-Greer-Thorbecke poverty indices as a product of the three components which should be involved in every poverty index: the incidence of poverty, measured by the headcount ratio, the intensity of poverty, measured by the aggregate income gap ratio and the inequality among the poor measured by an increasing transformation of the corresponding inequality index of the Generalized Entropy family. Then, taking data from the Spanish Household Budget Surveys (SHB) as a basis we show the advantages and possibilities of this framework in regard to completing and detailing information in studies of poverty over time.

A Consistent Multidimensional Generalization of the Pigou-Dalton Transfer Principle: An Analysis

This paper explores the implications of using multidimensional majorization criteria to derive inequality measures, without taking into consideration the idea behind the Pigou-Dalton principle, in the sense that if a richer person transfers something of at least one attribute to a poorer person the inequality falls. A new and basic criterion proposed by Fleurbaey and Trannoy (2003) which generalizes this idea to the multidimensional framework is explored, and its logical relationships with the dominance criteria that exist in the literature are analyzed. The paper also surveys the existent multidimensional inequality indices in order to see whether they meet this new criterion.

Multidimensional unit- and subgroup-consistent inequality and poverty measures: some characterizations

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 Tsuis 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.

An Axiomatic Characterization of the Theil Inequality Ordering

We identify an ordinal decomposability property and use it, along with other ordinal axioms, to characterize the Theil inequality ordering.

IKASYS: using mobile devices for memorization and training activities

Mobile learning (m-learning) integrates the current mobile computing technology with educational aspects to enhance the effectiveness of the traditional learning process. This paper describes IKASYS, an m-learning management tool that provides support for the whole cycle of memorization and training activities in a wide range of domains. The tool has been developed for being used in school-wide environments. This paper focuses mainly on IKASYS Trainer, the application for the mobile device.

Some characterisations of self-dual aggregation functions when relative shortfalls are considered

Abstract Whenever shortfalls are defined as the absolute difference between the upper bound and the level of attainments the characterisation of aggregation functions that rank attainment and shortfall distributions mirroring one another, i.e. self-dual aggregation functions, is a widely discussed issue. In this paper we consider an alternative definition of shortfalls as the relative difference between the upper bound and the level of attainments and extend some characterisation results to this new framework. Moreover, we propose a particular dual decomposition for each aggregation function and apply it to two major classes of homogeneous aggregation functions: α-power means and OWA operators.

A Dual Decomposition of Some Rank Dependent Social Evaluation Functions

In the context of the dual decomposition of the rank dependent social evaluation functions we examine the k-PTS principle introduced by Gajdos and introduce a new property with balanced sensitivity to both tails of the distribution. In particular we analyse its implications for the S-Gini family.