The 'income shortfall of each person below the poverty line' is a crucial component addressed by the Sen Measure (specifically related to the poverty gap part), which captures the depth or intensity of poverty, not just its incidence. By also incorporating inequality among the poor (through the Gini coefficient), the Sen Measure measures the distribution of welfare among the poor, reflecting that a society with the same headcount ratio might have different levels of welfare depending on how far below the line the poor are and how equally their poverty is distributed. This focus on the depth and distribution of poverty among the poor makes it a measure of welfare distribution among the disadvantaged group, rather than just overall wealth distribution.