Another Mere Addition Paradox? Some Reflections on Variable Population Poverty Measurement

Debates about poverty relief and foreign aid often hinge on claims about how many poor people there are in the world and what constitutes poverty. Good measures of poverty are essential for addressing the world poverty problem. Measures of poverty require a basis for determining who is poor and a method of aggregation. Historically, the methods of aggregation were quite simple. The headcount index (H), for instance, measures the number of poor people as a percentage of the total population. The poverty gap index for the whole population (I) takes the total aggregate shortfall from the poverty line divided by the number of people and the poverty line itself. Recently, however, economists have suggested several more complicated alternatives including Sen’s index, the Sen-Shorrocks-Thon (SST) index, and the Foster-Greer-Thorbecke (FGT) index (which, under some parameterizations is equivalent to H and I). This paper critiques several of the main poverty indexes in the literature by setting out and defending its ‘axiom’ (intuition or desiderata) for any good poverty measure. It argues that if Sen’s index, the SST, and the FGT indexes do not satisfy this ‘no mere addition axiom’, they do not provide compelling measures of anything that can intuitively be considered poverty. Next, it illustrates how these poverty indexes violate this no mere addition axiom. Finally, the paper illustrates one way of modifying the indexes to satisfy the no mere addition axiom with the FGT. It notes, however, that these alternatives will not do for all policy purposes. So, it is important to consider further how poverty indexes and axioms fare in variable population contexts.