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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TL;DR: The social choice problem as discussed by the authors deals with methods of marshalling information, particularly those relating to the people involved, to arrive at correct social judgments or acceptable group decisions, but the natures of the possible informational inputs vary, as do the required outputs of judgments, decisions or the required means of settlement.
Abstract: Publisher Summary This chapter discusses the social choice theory. There is social choice problems, which deals with methods of marshalling information, particularly those relating to the people involved, to arrive at correct social judgments or acceptable group decisions. But the natures of the possible informational inputs vary, as do the required outputs of judgments, decisions, or the required means of settlement. The balance of moral and pragmatic considerations also varies with the nature of the exercise. There are other differences, for example, whether the procedures permit the use of discretion in interpreting individual utilities or are mechanical. The nature of the exercise affects the appropriate specification of the social choice format. This relates to distinctions among structures such as social welfare functions, social decision functions, social choice functions or functional collective choice rules, or social welfare functional. It also affects the appropriateness of particular axioms within a given structure, for example, whether the social welfare function satisfies the independence condition or what types of interpersonal comparability if any is used. The relevance of the various results presented and discussed depends on the particular nature of the exercise to which application is sought.
113 citations
TL;DR: This paper reviews the operational research literature on inequity averse optimization and focuses on the cases where there is a tradeoff between efficiency and equity.
113 citations
Cites background from "On the Measurement of Inequality"
...…u is increasing and concave (Shorrocks, 1983; Rothschild & Stiglitz, 1973) Parts of Theorem 4 for the special case where ∑ i∈I y1i = ∑ i∈I y2i re proven by Atkinson (1970) and Dasgupta, Sen, and Starrett (1973) ased on the results by Hardy, Littlewood, and Polya (1934) on maorization (see also…...
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TL;DR: In Latin America, the Gini coefficient fell in 16 of the 17 countries where there are comparable data, and the change was statistically significant for all of them as mentioned in this paper, and the causes behind the decline in returns to schooling, however, have not been unambiguously established.
Abstract: Inequality in Latin America unambiguously declined in the 2000s. The Gini coefficient fell in 16 of the 17 countries where there are comparable data, and the change was statistically significant for all of them. Existing studies point to two main explanations for the decline in inequality: a reduction in hourly labor income inequality, and more robust and progressive government transfers. Available evidence suggests that it is the skill premium -- or, more precisely, the returns to primary, secondary, and tertiary education vs. no schooling or incomplete primary schooling -- that drives the decline in hourly labor income inequality. The causes behind the decline in returns to schooling, however, have not been unambiguously established. Some studies find that returns fell because of an increase in the supply of workers with more educational attainment; others, because of a shift in demand away from skilled labor.
112 citations
04 May 2020
TL;DR: In this article, the authors proposed a scheduling policy by jointly accounting for the staleness of the received parameters and the instantaneous channel qualities to improve the running efficiency of federated learning.
Abstract: Federated learning (FL) is a machine learning model that preserves data privacy in the training process. Specifically, FL brings the model directly to the user equipments (UEs) for local training, where an edge server periodically collects the trained parameters to produce an improved model and sends it back to the UEs. However, since communication usually occurs through a limited spectrum, only a portion of the UEs can update their parameters upon each global aggregation. As such, new scheduling algorithms have to be engineered to facilitate the full implementation of FL. In this paper, based on a metric termed the age of update (AoU), we propose a scheduling policy by jointly accounting for the staleness of the received parameters and the instantaneous channel qualities to improve the running efficiency of FL. The proposed algorithm has low complexity and its effectiveness is demonstrated by Monte Carlo simulations.
112 citations
TL;DR: In this article, the relationship between the inequality of income distributions and the social welfare they imply is investigated. But the authors focus on the trade-off between size and distribution of incomes.
112 citations
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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