Deprivation, welfare and inequality

2007

J Econ Inequal

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Section: Discussion Of Related Results In the Literaturementioning

confidence: 94%

An extended Gini approach to inequality measurement

2007

J Econ Inequal

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“…14 14 While this principle makes sense intuitively, it is subject to the same criticism as the one that has been addressed to the standard principle of transfers in the unidimensional framework. Namely, while the individuals involved in the transfer have become more equal, the inequalities between each of these two individuals and any other individual in the population has increased (see, e.g., [13,36]). Within-type progressive income transfer.…”

Section: Bidimensional Ordered Poverty Gap Dominancementioning

confidence: 99%

Ethically robust comparisons of bidimensional distributions with an ordinal attribute

Gravel

Journal of Economic Theory

2012

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We provide foundations for robust normative evaluation of distributions of two attributes, one of which is cardinally measurable and transferable between individuals and the other is ordinal and non-transferable. The result that we establish takes the form of an analogue to the standard Hardy-Littlewood-Pólya theorem for distributions of one cardinal attribute. More specifically, we identify the transformations of the distributions which guarantee that social welfare increases according to utilitarian unanimity provided that the utility function is concave in the cardinal attribute and that its marginal utility with respect to the same attribute is non-increasing in the ordinal attribute. We establish that this unanimity ranking of the distributions is equivalent to the ordered poverty gap quasi-ordering introduced by Bourguignon [12]. Finally, we show that, if one distribution dominates another according to the ordered poverty gap criterion, then the former can be derived from the latter by means of an appropriate and finite sequence of such transformations. Introductory remarksThe normative foundations of the comparison of distributions of a single attribute between a given number of individuals are by now well-established. They originate in the equivalence between three statements that are considered relevant answers to the question of when a distribution x can be considered normatively better than a distribution y. Given two distributions x and y with equal means, these statements, the equivalence of which was first established by Hardy et al. [30] and popularised later on among economists by Kolm [32], Atkinson [3], Dasgupta et al. [15], Sen [47], Fields and Fei [21] among others, are the following:(a) Distribution x can be obtained from distribution y by means of a finite sequence of progressive -or equivalently Pigou-Dalton -transfers. (b) All utilitarian ethical observers who assume that individuals convert the attribute into wellbeing by means of the same non-decreasing and concave utility function rank distribution x above distribution y. (c) The Lorenz curve of distribution x lies nowhere above and somewhere below that of y, or equivalently, for all poverty lines, the poverty gap is no greater in distribution x than in distribution y and it is smaller for at least one poverty line.This remarkable result, which can be generalised in a number of ways, points to three different aspects of the inequality measurement process. 1 The first statement aims at capturing the very notion of inequality reduction by associating it with elementary transformations of the distributions. The second statement is fundamentally normative and it assumes that society has an aversion to inequality which, in the utilitarian framework, is reflected by the concavity of the utility function. To some extent the first statement helps in clarifying the meaning of the restriction imposed on the utility function in the second statement. While these two conditions shed light on two different facets of the inequality concept, they do ...

“…6 Integrating twice from s to s the decumulative distribution functions and comparing the values obtained for all s provide a practical means for checking if one profile is unanimously preferred to another when attention is restricted to value functions whose first derivative is positive, non-decreasing and 5 Actually one only needs n = 3 in order to prove that v convex is necessary for performance to increase as the result of an augmenting regressive transfer (see e.g. Moyes and Shorrocks (1994)) 6 The dominance criteria based on the quantile functions are related to the dual model of choice under risk introduced by Yaari (1987) and exploited later in the inequality literature by Ebert (1988), Yaari (1988) and more recently by Moyes (2004, 2006) and Magdalou and Moyes (2009). convex.…”

Section: Theorem 32 Let X Y ∈ S (D)mentioning

confidence: 99%

Elitism and stochastic dominance

Bazen

2011

Soc Choice Welf

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RésuméLa dominance stochastique est traditionellement associée à la mesure du risque et de l'inégalité et repose sur la concavité de la fonction d'utilité. Nous prétendons que l'approche en terme de dominance stochastique a des implications qui vont au-delà de la mesure du risque et de l'inégalité pour peu que l'on procède à certains ajustements. Nous appliquons ici la dominance stochastique à la mesure de l'élitisme, notion qui peut d'une certaine manière être considérée comme le contraire de l'égalitarisme. Alors que les critères de dominance stochastique habituels accordent plus de valeur aux distributions qui sont à la fois moins inégales et plus efficientes, nos critères garantissent qu'une distribution sera d'autant mieux classée qu'une autre qu'elle est à la fois plus efficiente et plus inégale. Afin d'illustrer notre approche, nous proposons deux exemples : (i) la comparaison d'une vingtaine de départements d'économie en Europe du point de vue de la performance scientifique, et (ii) la comparaison de différents pays sur la base de la notion d'affluence par opposition à celle de pauvreté.Mots Clé : Fonction de Distribution Décumulative, Stochastic Dominance, Transfers Régressifs, Élitisme, Performance Scientifique, Affluence. Elitism and Stochastic DominanceAbstract Stochastic dominance has been typically used with a special emphasis on risk and inequality reduction something captured by the concavity of the utility function in the expected utility model. We claim that the applicability of the stochastic dominance approach goes far beyond risk and inequality measurement provided suitable adaptations be made. We apply in the paper the stochastic dominance approach to the measurement of elitism which may be considered the opposite of egalitarianism. While the usual stochastic dominance quasi-orderings attach more value to more equal and more efficient distributions, our criteria ensure that, the more unequal and the more efficient the distribution, the higher it is ranked. Two instances are provided by (i) comparisons of scientific performance across institutions like universities or departments, and (ii) comparisons of affluence as opposed to poverty between countries.Journal of Economic Literature Classification Number: D31, D63.