Notes on the measurement of inequality

Dasgupta, Partha; Sen, Amartya; Starrett, David A.

doi:10.1016/0022-0531(73)90033-1

Cited by 537 publications

(196 citation statements)

References 6 publications

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“…Since m z m u b 0, and f Á is any arbitrary S-concave function, we conclude that uLz (see Dasgupta et al 1973).…”

Section: Appendixmentioning

confidence: 84%

Intermediate inequality and welfare

Río¹,

Ruiz‐Castillo²

2000

Social Choice and Welfare

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Abstract. We introduce a new centrist or intermediate inequality concept, between the usual relative and absolute notions, which is shown to be a variant of the -ray invariant inequality measures in P®ngsten and Seidl (1997). We say that distributions x and y have the same xY p -inequality if the total income di¨erence between them is allocated among the individuals as follows: 100p% preserving income shares in x, and 100 1 À p % in equal absolute amounts. This notion can be made as operational as current standard methods in Shorrocks (1983).

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“…Since m z m u b 0, and f Á is any arbitrary S-concave function, we conclude that uLz (see Dasgupta et al 1973).…”

Section: Appendixmentioning

confidence: 84%

Intermediate inequality and welfare

Río¹,

Ruiz‐Castillo²

2000

Social Choice and Welfare

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“…For extensive discussions and alternative proofs of this theorern, we refer the reader tú Dasgupta et al (1973), Rotschild and Stiglitz (1973), Fields and Fei (1978), Foster (1985), Marshall and Olkin (1979), Arnold (1987) and Pecaric et al (1992).…”

Section: The Fundamental Theorem Of Inequality Economicsmentioning

confidence: 99%

“…From the seminal contributions ofKolm (1969), Atkinson (1970), Dasgupta et al (1973), and Rotschild and Stiglitz (1973), a minimal consensus has emerged. A ranking of income distributions should be consistent with the Lorenz partial ordering, for this ordering is supported by all inequality averse welfare functionals, and it is the only ordering which is consistent with our intuition that rank-preserving transfers from rich to poor should decrease inequality.…”

Section: Introductionmentioning

confidence: 99%

The measurement of opportunity inequality: a cardinality-based approach

Kranich

1998

Social Choice and Welfare

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_We consider the problem of ranking distributions of opportunity sets on the basis of equality.First, conditional on agents' preferences over individual opportunity sets, we formulate the analogues ofthe notions ofthe Lorenz partial ordering, equalizing Dalton transfers, and inequality averse social welfare functionals -concepts which play a central role in the literature on income inequality. For the particular case in which agents rank opportunity sets on the basis of their cardinalities, we establish an 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 equalizing transfers, and if and only if the former is ranked higher than the latter by all inequality averse social welfare functionals. In addition, we characterize the smallest monotonic and transitive extension of the cardinality-based Lorenz inequality ordering.

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“…Proof See [6], p. 182. Let 1 (Sh, [0, 1]) be the set of continuous and strictly Schur-convex functions defined on S h and taking their values in [0, 1].…”

Section: (2) Y = Bx Where B Is a Bistochastic Matrix Of Order H Sumentioning

confidence: 99%

“…The Dalton's "principle of transfers" means that a finite sequence of transformations transferring income from the rich to the poor, should decrease the value of the inequality measure. A theorem by Hardy, Littlewood and Polya, spelt out in Dasgupta, Sen and Starrett [6], shows that the requirement of Dalton's "principle of transfers" is equivalent to the mathematical property of strict Schur-convexity.…”

Section: Introductionmentioning

confidence: 99%

Topological aggregation of inequality preorders

Breton

Trannoy

Uriarte³

1985

Soc Choice Welfare

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Abstract. An inequality preorder is defined as a complete preorder on a simplex which satisfies the properties of continuity and strict Schur-convexity (the mathematical equivalent of Dalton's "principle of transfers"). The paper shows that it is possible to aggregate individual inequality preorders into a collective one if we are interested in continuous anonymous aggregation rules that respect unanimity. The aggregation problem is studied within a topological framework introduced by Chichilnisky.

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Notes on the measurement of inequality

Cited by 537 publications

References 6 publications

Intermediate inequality and welfare

Intermediate inequality and welfare

The measurement of opportunity inequality: a cardinality-based approach

Topological aggregation of inequality preorders

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