论文标题
洛伦兹地图，基于多维重排的不平等排序和曲线
Lorenz map, inequality ordering and curves based on multidimensional rearrangements
论文作者
论文摘要
我们提出了基于最佳运输理论的多元重排的洛伦兹曲线的多元扩展。我们将矢量洛伦兹图定义为与多元资源分配相关的向量分位图的积分。洛伦兹地图的每个组成部分都是每个资源的累积份额，如传统的单变量情况。此类洛伦兹地图的点序订购定义了一个新的多元大型化顺序，这等同于任何具有不平等的社会规划师的偏爱，依赖多元等级依赖性社会评估功能。我们定义了一个多属性Gini指数的家族，并根据Lorenz地图进行完整订购。我们提出了逆洛伦兹函数的水平集，作为可视化和比较二维不平等的实用工具，并将其应用于1989年至2022年之间美国的收入不平等。
We propose a multivariate extension of the Lorenz curve based on multivariate rearrangements of optimal transport theory. We define a vector Lorenz map as the integral of the vector quantile map associated with a multivariate resource allocation. Each component of the Lorenz map is the cumulative share of each resource, as in the traditional univariate case. The pointwise ordering of such Lorenz maps defines a new multivariate majorization order, which is equivalent to preference by any social planner with inequality averse multivariate rank dependent social evaluation functional. We define a family of multi-attribute Gini index and complete ordering based on the Lorenz map. We propose the level sets of an Inverse Lorenz Function as a practical tool to visualize and compare inequality in two dimensions, and apply it to income-wealth inequality in the United States between 1989 and 2022.
