On the Measurement of Inequality
TL;DR: In this paper, the problem of comparing two frequency distributions f(u) of an attribute y which for convenience I shall refer to as income is defined as a risk in the theory of decision-making under uncertainty.
About: This article is published in Journal of Economic Theory.The article was published on 1970-09-01. It has received 5002 citations till now. The article focuses on the topics: Income inequality metrics & Income distribution.
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19 Jul 2018
TL;DR: This work demonstrates that minimizing exclusively the between-group component may, in fact, increase the within-group, and hence the overall unfairness, and describes and illustrates the tradeoffs between the measures of (un)fairness and the prediction accuracy.
Abstract: Discrimination via algorithmic decision making has received considerable attention. Prior work largely focuses on defining conditions for fairness, but does not define satisfactory measures of algorithmic unfairness. In this paper, we focus on the following question: Given two unfair algorithms, how should we determine which of the two is more unfair? Our core idea is to use existing inequality indices from economics to measure how unequally the outcomes of an algorithm benefit different individuals or groups in a population. Our work offers a justified and general framework to compare and contrast the (un)fairness of algorithmic predictors. This unifying approach enables us to quantify unfairness both at the individual and the group level. Further, our work reveals overlooked tradeoffs between different fairness notions: using our proposed measures, the overall individual-level unfairness of an algorithm can be decomposed into a between-group and a within-group component. Earlier methods are typically designed to tackle only between-group un- fairness, which may be justified for legal or other reasons. However, we demonstrate that minimizing exclusively the between-group component may, in fact, increase the within-group, and hence the overall unfairness. We characterize and illustrate the tradeoffs between our measures of (un)fairness and the prediction accuracy.
208 citations
TL;DR: In this article, the authors show that widely used summary measures of inequality or the idea of the "disappearing middle class" are potentially misleading by failing to distinguish between the concepts of inequality and polarization, and using scalar "inequality" measures which are not consistent with rankings based on Lorenz curves.
Abstract: Widely used summary measures of inequality or the idea of the “disappearing middle class” are potentially misleading. Divergences between evidence cited and conclusions drawn include failing to distinguish between the concepts of inequality and polarization, and using scalar “inequality” measures which are not consistent with rankings based on Lorenz curves. In addition, inappropriate claims about trends in inequality can arise from focusing on only a sub-population such as full-time male workers, and failing to account for sampling variability. These divergences are illustrated using Canadian data on labour incomes over the 1967 to 1994 period.
206 citations
TL;DR: The authors introduced a new index of poverty, which satisfies all the axioms for "a good index" of poverty and showed that the index satisfies all of the criteria for a good index.
205 citations
01 Jan 1999
TL;DR: This article addresses the question of whether the authors should be measuring health inequalities or social group health differences and reviews some of the major arguments for and against each of them.
Abstract: Both health inequalities and social group health differences are important aspects of measuring population health. Despite widespread recognition of their magnitude in many high- and low-income countries, there is considerable debate about the meaning and measurement of health inequalities, social group health differences and inequities. The lack of standard definitions, measurement strategies and indicators has and will continue to limit comparisons — between and within countries, and over time — of health inequalities, and perhaps more importantly comparative analyses of their determinants. Such comparative work, however, will be essential to find effective policies for governments to reduce health inequalities. This article addresses the question of whether we should be measuring health inequalities or social group health differences. To help clarify the strengths and weaknesses of these two approaches, we review some of the major arguments for and against each of them.
205 citations
25 Mar 2012
TL;DR: Two families of fairness functions are developed that provide different tradeoffs, characterize the effect of user requests' heterogeneity, and prove conditions under which these fairness measures satisfy the Pareto efficiency, sharing incentive, and envy-free properties.
Abstract: Quantifying the notion of fairness is under-explored when users request different ratios of multiple distinct resource types. A typical example is datacenters processing jobs with heterogeneous resource requirements on CPU, memory, etc. A generalization of max-min fairness to multiple resources was recently proposed in [1], but may suffer from significant loss of efficiency. This paper develops a unifying framework addressing this fairness-efficiency tradeoff with multiple resource types. We develop two families of fairness functions which provide different tradeoffs, characterize the effect of user requests' heterogeneity, and prove conditions under which these fairness measures satisfy the Pareto efficiency, sharing incentive, and envy-free properties. Intuitions behind the analysis are explained in two visualizations of multi-resource allocation.
203 citations
References
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TL;DR: In this article, a measure of risk aversion in the small, the risk premium or insurance premium for an arbitrary risk, and a natural concept of decreasing risk aversion are discussed and related to one another.
Abstract: This paper concerns utility functions for money. A measure of risk aversion in the small, the risk premium or insurance premium for an arbitrary risk, and a natural concept of decreasing risk aversion are discussed and related to one another. Risks are also considered as a proportion of total assets.
5,207 citations
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1,748 citations
"On the Measurement of Inequality" refers background in this paper
...3 See Rothschild and Stiglitz [13], Hadar and Russell [ 5 ], and Hanoch and Levy [6]....
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1,738 citations
"On the Measurement of Inequality" refers methods in this paper
...Then by applying the results of Pratt [l 11, Arrow [ 2 ], and others, we can see that this requirement (which may be referred to as constant (relative) inequality-aversion) implies that U(y) has the form...
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1,544 citations
TL;DR: In this paper, an analysis of the first step of the decision-making process of an individual decision maker among alternative risky ventures is presented, in terms of a single dimension such as money, both for the utility functions and for the probability distributions.
Abstract: Publisher Summary The choice of an individual decision maker among alternative risky ventures may be regarded as a two-step procedure. The decision maker chooses an efficient set among all available portfolios, independently of his tastes or preferences. Then, the decision maker applies individual preferences to this set to choose the desired portfolio. The subject of this chapter is the analysis of the first step. It deals with optimal selection rules that minimize the efficient set by discarding any portfolio that is inefficient in the sense that it is inferior to a member of the efficient set, from point of view of each and every individual, when all individuals' utility functions are assumed to be of a given general class of admissible functions. The analysis presented in the chapter is carried out in terms of a single dimension such as money, both for the utility functions and for the probability distributions. However, the results may easily be extended, with minor changes in the theorems and the proofs, to the multivariate case. The chapter explains a necessary and sufficient condition for efficiency, when no further restrictions are imposed on the utility functions. It presents proofs of the optimal efficiency criterion in the presence of general risk aversion, that is, for concave utility functions.
1,160 citations