The axioms used to characterize the generalized Gini social evaluation orderings for one-dimensional distributions are extended to the multidimensional attributes case. A social evaluation ordering is shown to have a …
The axioms used to characterize the generalized Gini social evaluation orderings for one-dimensional distributions are extended to the multidimensional attributes case. A social evaluation ordering is shown to have a two-stage aggregation representation if these axioms and a separability assumption are satisfied. In the first stage, the distributions of each attribute are aggregated using generalized Gini social evaluation functions. The functional form of the second-stage aggregator depends on the number of attributes and on which version of a comonotonic additivity axiom is used. The implications of these results for the corresponding multidimensional indices of relative and absolute inequality are also considered.
Abstract When incomes are ranked in descending order the social-evaluation function corresponding to the Gini relative inequality index can be written as a linear function withthe weights being the odd …
Abstract When incomes are ranked in descending order the social-evaluation function corresponding to the Gini relative inequality index can be written as a linear function withthe weights being the odd numbers in increasing order. We generalize this function by allowing the weights to be an arbitrary non-decreasing sequence of numbers. This results in a class of generalized Gini relative inequality indices and a class of generalized Gini absolute inequality indices. An axiomatic characterization of the latter class is also provided.
The axioms used to characterize the generalized Gini social evaluation orderings for one-dimensional distributions are extended to the multidimensional attributes case. A social evaluation ordering is shown to have a …
The axioms used to characterize the generalized Gini social evaluation orderings for one-dimensional distributions are extended to the multidimensional attributes case. A social evaluation ordering is shown to have a two-stage aggregation representation if these axioms and a separability assumption are satisfied. In the first stage, the distributions of each attribute are aggregated using generalized Gini social evaluation functions. The functional form of the second-stage aggregator depends on the number of attributes and on which version of a comonotonic additivity axiom is used. The implications of these results for the corresponding multidimensional indices of relative and absolute inequality are also considered.
Abstract When incomes are ranked in descending order the social-evaluation function corresponding to the Gini relative inequality index can be written as a linear function withthe weights being the odd …
Abstract When incomes are ranked in descending order the social-evaluation function corresponding to the Gini relative inequality index can be written as a linear function withthe weights being the odd numbers in increasing order. We generalize this function by allowing the weights to be an arbitrary non-decreasing sequence of numbers. This results in a class of generalized Gini relative inequality indices and a class of generalized Gini absolute inequality indices. An axiomatic characterization of the latter class is also provided.
Two essential intuitions about the concept of multidimensional inequality have been highlighted in the emerging body of literature on this subject: first, multidimensional inequality should be a function of the …
Two essential intuitions about the concept of multidimensional inequality have been highlighted in the emerging body of literature on this subject: first, multidimensional inequality should be a function of the uniform inequality of a multivariate distribution of goods or attributes across people (Kolm, 1977); and second, it should also be a function of the cross-correlation between distributions of goods or attributes in different dimensions (Atkinson and Bourguignon, 1982; Walzer, 1983). While the first intuition has played a major role in the design of fully-fledged multidimensional inequality indices, the second one has only recently received attention (Tsui, 1999); and, so far, multidimensional generalized entropy measures are the only inequality measures known to respect both intuitions. The present paper proposes a general method of designing a wider range of multidimensional inequality indices that also respect both intuitions and illustrates this method by defining two classes of such indices: a generalization of the Gini coefficient, and a generalization of Atkinsons one-dimensional measure of inequality.
In this paper we shall study the concept of cardinal utility in three different situations (stochastic objects of choice, stochastic act of choice; independent factors of the action set) by …
In this paper we shall study the concept of cardinal utility in three different situations (stochastic objects of choice, stochastic act of choice; independent factors of the action set) by means of the same mathematical result that gives a topological characterization of three families of parallel straight lines in a plane. This result, proved first by G. Thomsen [24] under differentiability assumptions, and later by W. Blaschke [2] in its present general form (see also W. Blaschke and G. Bol [3]), can be briefly described as follows. Consider the topological image G of a two-dimensional convex set and three families of curves in that set such that (a) exactly one curve of each family goes through a point of G, and (b) two curves of different families have at most one common point. Is there a topological transformation carrying these three families of curves into three families of parallel straight lines? If the answer is affirmative, the hexagonal configuration of Figure l(a) is observed. Let P be an arbitrary point of G, draw through it a curve of each family, and take an arbitrary point A on one of these curves; by drawing through A the curves of the other two families, we may obtain B and B' and from them C and C'.
Journal Article Additive Utility Functions and Linear Engel Curves Get access Robert A. Pollak Robert A. Pollak University of Pennsylvania Search for other works by this author on: Oxford Academic …
Journal Article Additive Utility Functions and Linear Engel Curves Get access Robert A. Pollak Robert A. Pollak University of Pennsylvania Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 38, Issue 4, October 1971, Pages 401–414, https://doi.org/10.2307/2296686 Published: 01 October 1971