Poverty without poverty line

I propose a new cardinal measure of poverty, which builds on the intuitive notion that a person with half the income of another is twice as poor. Mathematically, this implies that poverty is the reciprocal of income. The resulting aggregate measure has a simple interpretation: it is the average number of days needed to get a reference level of income. I call the measure average poorness, to reflect the fact that poverty is a spectrum and not a binary status. The new measure has excellent properties, being additively decomposable in population subgroups, fully accounting for the depth and severity of poverty, and generating orderings and comparisons that are robust to the choice of reference level of income. Using data from a survey experiment, I show that the new measure is consistent with how a majority of experts and members of the public think about poverty.