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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47 citations
01 Sep 2003
TL;DR: This work theoretically and empirically evaluate twelve diversity measures used as heuristic measures of interestingness for ranking summaries generated from databases, and describes five principles that any measure must satisfy to be considered useful forranking summaries.
Abstract: When mining a large database, the number of patterns discovered can easily exceed the capabilities of a human user to identify interesting results. To address this problem, various techniques have been suggested to reduce and/or order the patterns prior to presenting them to the user. In this paper, our focus is on ranking summaries generated from a single dataset, where attributes can be generalized in many different ways and to many levels of granularity according to taxonomic hierarchies. We theoretically and empirically evaluate twelve diversity measures used as heuristic measures of interestingness for ranking summaries generated from databases. The twelve diversity measures have previously been utilized in various disciplines, such as information theory, statistics, ecology, and economics. We describe five principles that any measure must satisfy to be considered useful for ranking summaries. Theoretical results show that the proposed principles define a partial order on the ranked summaries in most cases, and in some cases, define a total order. Theoretical results also show that seven of the twelve diversity measures satisfy all of the five principles. We empirically analyze the rank order of the summaries as determined by each of the twelve measures. These empirical results show that the measures tend to rank the less complex summaries as most interesting. Finally, we analyze the distribution of the index values generated by each of the twelve diversity measures. Empirical results, obtained using synthetic data, show that the distribution of index values generated tend to be highly skewed about the mean, median, and middle index values. Finally, we demonstrate a technique, based upon our principles, for visualizing the relative interestingness of summaries. The objective of this work is to gain some insight into the behaviour that can be expected from our principled approach in practice.
47 citations
Cites methods from "On the Measurement of Inequality"
...Diversity measures have also been used by economists and social scientists to study the distribution of income between different socioeconomic groups or geographical regions [3, 5, 15, 64]....
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...The IAtkinson measure, based upon a measure of inequality from economics [5], measures the percentage to which the population in a summary would have to be increased to achieve the same level of interestingness if the counts in the summary were uniformly distributed....
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TL;DR: In this article, a single class of utility functions with risk-aversion as sole parameter emerges when risk aversion is regarded as a function of the present wealth, rather than subject to alteration through imagining possible future wealths.
47 citations
TL;DR: In this paper, the authors provide an economic analysis of racial bias in police stops and searches and develop a model of policing behavior, which is used to define discrimination, clarify its nature and identify its sources.
46 citations
TL;DR: In this article, the authors evaluate the distributional and welfare effects of two recent changes of VAT and excise taxes in Italy applying and comparing two related and complementary methods of analysis: the first based on distributional characteristics of Feldstein(1972) and recently applied by Newbery (1995); the second basedon the theory of marginal dominance developed by Mayshar andYitzhaki (1996).
Abstract: This paper evaluatesthe distributional and welfare effects of two recent changesof Value Added Tax (VAT) and excise taxes in Italy applying andcomparing two related and complementary methods of analysis:the first based on the distributional characteristics of Feldstein(1972) and recently applied by Newbery (1995); the second basedon the theory of marginal dominance developed by Mayshar andYitzhaki (1996). The paper finds no evidence that the reformshave redistributed purchasing power among households. But themost striking result is that a simpler two-rate VAT structure,set according to the European directives on VAT coordination,could have replaced the present system producing the same revenueand increasing welfare. This last result provides a clear instancein which reducing the number of VAT rates can be welcome evenin the presence of distributional concerns.
46 citations
Cites background from "On the Measurement of Inequality"
...The basis of this approach lies in the stochastic dominance theory developed by Hanoch and Levy (1969) and extended to income distribution comparisons by Atkinson (1970) and Shorrocks (1983)....
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...Welfare changes can be readily estimated provided that a functional form for the SWF can be agreed upon, for example the Atkinson (1970) social welfare function WD P h .v...
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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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"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