Multidimensional polarization for ordinal data

Western governments increasingly place more emphasis on non-income dimensions in measuring national well-being (e.g. the UK, France). Not only averages, but the characteristics of the whole distribution (e.g. inequalities) are taken into consideration. Commonly used data such as life satisfaction, declared health status or level of education, however, are ordinal in nature and the fundamental problem of measuring inequality with ordinal variables exists. Here, a class of multidimensional inequality indices for ordinal data is characterized by inequality axioms and based on the characterization theorem an inequality measure is proposed. The method ensures that the index is also attribute decomposable, that is, we can estimate the contribution to overall inequality from inequality in dimensions and from their association. It was found for the period 1972-2010 in the US, excluding 1985 that inequality in perceived happiness contributed more to overall inequality than health inequality. Joint inequality in health and happiness was significantly higher in the first half of the study period (0.3 vs. 0.2). In the 1970s and 1980s most healthy people were also happier and this positive association increased inequality by around 20 percent. This trend was reversed in the late 1980s when the contribution of association became negative. This trend for the healthiest to no longer be the happiest persisted with the exception of three years.