Multidimensional Poverty Index

The first cutoff is within each indicator: a person is deprived in indicator j if their achievement falls below that indicator's threshold z_j (for example, no household member completed primary school). The second cutoff is across dimensions: a person counts as multidimensionally poor only if their weighted deprivation score reaches the poverty cutoff k (for example, deprived in at least one third of weighted indicators). The first defines deprivation indicator by indicator; the second defines who is poor overall, ensuring the measure reflects joint deprivation.

The simple multidimensional headcount H counts who is poor but is insensitive to how broadly each poor person is deprived — if a poor person escapes one deprivation but remains above the cutoff k, H does not move. The adjusted headcount M0 = H times A multiplies incidence by intensity, so it falls whenever any poor person reduces their deprivations. This dimensional monotonicity is the key axiomatic advantage and the reason M0, not H, is the headline measure of the Alkire-Foster method.

Both are normative choices made by the analyst or institution. The global MPI, for example, uses three equally weighted dimensions (health, education, living standards) with equal weights within each, and sets k at one third of weighted indicators. These choices are defensible but not unique, and the index can be sensitive to them, so good practice is to justify the choices transparently and report robustness over alternative weights and a range of k values rather than presenting a single configuration as definitive.