- Title Pages
- Dedication
- Preface to the First Edition
- Preface to the Enlarged Edition
- 1 Welfare Economics, Utilitarianism, and Equity
- 2 Measures of Inequality
- 3 Inequality as a Quasi‐Ordering
- 4 Work, Needs, and Inequality
- On Economic Inequality After a Quarter Century
- A.1.1 Prologue
- A.1.2 The 1973 Themes
- A.1.3 Further Issues
- A.2.1 Welfare as a Basis for Inequality Measurement
- A.2.2 From Welfare to Inequality
- A.2.3 From Inequality to Welfare
- A.3.1. Partial Rankings and Intersection Quasi‐Orderings
- A.3.2 Generalized Lorenz Dominance
- A.3.3 Stochastic Dominance
- A.4.1 The Class of Relative Inequality Measures
- A.4.2 Lorenz Dominance and Relative Inequality
- A.4.3 Transfer Sensitivity
- A.5.1 Decomposability
- A.5.2 Subgroup Consistency
- A.5.3 Consistency and interdependence
- A.6.1 Poverty: Identification and Aggregation
- A.6.2 Classical Poverty Aggregation: Head Count and Income Gap
- A.6.3 Relative Deprivation and the S Measure of Poverty
- A.6.4 Continuity, Transfers, and the S<sup>*</sup> Measure
- A.6.5 Decomposability, Subgroups, and the P<sub>α</sub> Measures
- A.6.6 Poverty Orderings
- A.7.1 Inequality, Welfarism, and Justice
- A.7.2 Functionings and Capabilities
- A.7.3 On Weights and Valuations
- A.7.4 Poverty as Capability Failure
- A.7.5 Indirect Assessment and Ordinal Intensity
- A.7.6 A Final Remark
- Bibliography
- Index of Names
- Subject Index

# Inequality as a Quasi‐Ordering

# Inequality as a Quasi‐Ordering

- Chapter:
- (p.47) 3 Inequality as a Quasi‐Ordering
- Source:
- On Economic Inequality
- Author(s):
### Amartya Sen (Contributor Webpage)

- Publisher:
- Oxford University Press

It is argued that the difficulty of using the positive and normative measures of inequality described in the previous chapter arises from the fact that they are ‘complete’ measures. Each of these measures may give absurd results, because they aim to give a complete‐ordering representation to a concept that is essentially one of partial ranking. Hence, a weakening of the inequality measures to a mixture of partly descriptive and partly normative considerations is proposed. A number of reasons for taking inequality rankings as quasi‐orderings rather than complete orderings are suggested.

*Keywords:*
descriptive measures, economic inequality, inequality, measurement, normative measures, positive measures, quasi‐ordering, ranking

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- Title Pages
- Dedication
- Preface to the First Edition
- Preface to the Enlarged Edition
- 1 Welfare Economics, Utilitarianism, and Equity
- 2 Measures of Inequality
- 3 Inequality as a Quasi‐Ordering
- 4 Work, Needs, and Inequality
- On Economic Inequality After a Quarter Century
- A.1.1 Prologue
- A.1.2 The 1973 Themes
- A.1.3 Further Issues
- A.2.1 Welfare as a Basis for Inequality Measurement
- A.2.2 From Welfare to Inequality
- A.2.3 From Inequality to Welfare
- A.3.1. Partial Rankings and Intersection Quasi‐Orderings
- A.3.2 Generalized Lorenz Dominance
- A.3.3 Stochastic Dominance
- A.4.1 The Class of Relative Inequality Measures
- A.4.2 Lorenz Dominance and Relative Inequality
- A.4.3 Transfer Sensitivity
- A.5.1 Decomposability
- A.5.2 Subgroup Consistency
- A.5.3 Consistency and interdependence
- A.6.1 Poverty: Identification and Aggregation
- A.6.2 Classical Poverty Aggregation: Head Count and Income Gap
- A.6.3 Relative Deprivation and the S Measure of Poverty
- A.6.4 Continuity, Transfers, and the S<sup>*</sup> Measure
- A.6.5 Decomposability, Subgroups, and the P<sub>α</sub> Measures
- A.6.6 Poverty Orderings
- A.7.1 Inequality, Welfarism, and Justice
- A.7.2 Functionings and Capabilities
- A.7.3 On Weights and Valuations
- A.7.4 Poverty as Capability Failure
- A.7.5 Indirect Assessment and Ordinal Intensity
- A.7.6 A Final Remark
- Bibliography
- Index of Names
- Subject Index