Income poverty measures with relative poverty lines

I derive poverty indices taking into account both the absolute and relative aspects of income well-being. The trade-off made by the social planner between those two aspects is captured at individual level by a well-being ordering. This ordering evaluates the well-being of an agent based on her income and a reference statistic on the income distribution, typically the mean. A family of poverty indices respecting the judgements held in the ordering is axiomatically characterized. Then, I study the consequences of requiring the poverty indices to grant a minimal precedence to the absolute over the relative aspect of income well-being. This compelling requirement has strong implications. In particular, the Poverty Gap Ratio is the only index in the popular Foster-Greer-Thorbecke family to satisfy it