Apouey Benedicte
Paris School of Economics (PSE).
Health Econ. 2007 Sep;16(9):875-94. doi: 10.1002/hec.1284.
This paper proposes an axiomatic foundation for new measures of polarization that can be applied to ordinal distributions such as self-assessed health (SAH) data. This is an improvement over the existing measures of polarization that can be used only for cardinal variables. The new measures of polarization avoid one difficulty that the related measures for evaluating health inequalities face. Indeed, inequality measures are mean based, and since only cardinal variables have a mean, SAH has to be cardinalized to compute a mean, which can then be used to calculate an inequality measure. In contrast, the new polarization measures are median based and hence do not require to impose cardinal scaling on the categories. After deriving the properties of these new polarization measures, we provide an empirical illustration using data from the British Household Panel Survey that demonstrates that SAH polarization is also a relevant question on empirical grounds, and that the polarization measures are adequate to evaluate polarization phenomena whereas inequality measures are not adequate in these cases.
本文为极化新测度提出了一个公理基础，该测度可应用于诸如自我评估健康（SAH）数据等序数分布。这是对现有仅可用于基数变量的极化测度的一种改进。新的极化测度避免了评估健康不平等的相关测度所面临的一个难题。事实上，不平等测度基于均值，由于只有基数变量有均值，所以SAH必须进行基数化处理以计算均值，进而用于计算不平等测度。相比之下，新的极化测度基于中位数，因此不需要对类别施加基数缩放。在推导这些新极化测度的性质之后，我们使用英国家庭追踪调查的数据进行了实证说明，结果表明SAH极化在实证层面也是一个相关问题，并且极化测度足以评估极化现象，而在这些情况下不平等测度并不适用。
