مقایسهٔ روش‌ها

	Multidimensional Poverty Index	Shapley Decomposition of Inequality
حوزه	اقتصاد	اقتصاد
خانواده	Process / pipeline	Process / pipeline
سال پیدایش	2011	2013
پدیدآور	Sabina Alkire & James Foster	Anthony Shorrocks (working paper 1999; published 2013)
نوع	Counting-based multidimensional poverty measure	Axiomatic decomposition procedure
منبع بنیادین	Alkire, S., & Foster, J. (2011). Counting and multidimensional poverty measurement. Journal of Public Economics, 95(7–8), 476–487.	Shorrocks, A. F. (2013). Decomposition procedures for distributional analysis: a unified framework based on the Shapley value. Journal of Economic Inequality, 11(1), 99–126.
نام‌های دیگر	MPI, Alkire-Foster Method, Adjusted Headcount Ratio, Dual-Cutoff Multidimensional Poverty	Shapley Decomposition, Shorrocks Shapley Decomposition, Factor Decomposition of Inequality, Shapley Value Distributional Decomposition
مرتبط	3	4
خلاصه	The Multidimensional Poverty Index applies the Alkire-Foster method, introduced by Sabina Alkire and James Foster in 2011, to measure poverty as the joint deprivation of individuals across several dimensions such as health, education, and living standards. Its signature is a dual-cutoff identification: a person is deprived in an indicator if they fall below that indicator's cutoff, and they are counted as multidimensionally poor only if their weighted count of deprivations crosses a cross-dimensional cutoff k. The headline measure is the adjusted headcount ratio M0 = H times A, the product of the share of people who are poor (incidence) and the average breadth of their deprivations (intensity).	The Shapley decomposition, formalized for distributional analysis by Anthony Shorrocks (in a widely circulated 1999 working paper, published in 2013), is a general procedure for attributing an inequality or poverty statistic to its contributing factors — income sources, population subgroups, or determinants. It borrows the Shapley value from cooperative game theory: each factor's contribution is its average marginal effect on the indicator across all possible orders in which factors could be eliminated. The result is an exact, symmetric, residual-free decomposition that applies to any indicator, even those (like the Gini) that have no natural analytic decomposition of their own.