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This paper presents axiomatic arguments to make the case for distribution-sensitive multidimensional poverty measures. The commonly-used counting measures violate the strong transfer axiom which requires regressive transfers to be unambiguously poverty-increasing and they are also invariant to changes in the distribution of a given set of deprivations amongst the poor. The paper appeals to strong transfer as well as an additional cross-dimensional convexity property to offer axiomatic justification for distribution-sensitive multidimensional poverty measures. Given the nonlinear structure of these measures, it is al also shown how the problem of an exact dimensional decomposition can be solved using Shapley decomposition methods to assess dimensional contributions to poverty. An empirical illustration for India highlights distinctive features of the distribution-sensitive measures.

Crossdimensional Convexity --- Multidimensional Poverty --- Poverty Assessment --- Poverty Measurement --- Poverty Reduction --- Shapley Decomposition --- Transfer Axiom

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Disjunctive Programming is a technique and a discipline initiated by the author in the early 1970's, which has become a central tool for solving nonconvex optimization problems like pure or mixed integer programs, through convexification (cutting plane) procedures combined with enumeration. It has played a major role in the revolution in the state of the art of Integer Programming that took place roughly during the period 1990-2010. The main benefit that the reader may acquire from reading this book is a deeper understanding of the theoretical underpinnings and of the applications potential of disjunctive programming, which range from more efficient problem formulation to enhanced modeling capability and improved solution methods for integer and combinatorial optimization. Egon Balas is University Professor and Lord Professor of Operations Research at Carnegie Mellon University's Tepper School of Business. .

Integer programming. --- Linear programming. --- Convex domains. --- Convex regions --- Convexity --- Calculus of variations --- Convex geometry --- Point set theory --- Production scheduling --- Programming (Mathematics) --- Matrix theory. --- Mathematics. --- Algorithms. --- Combinatorics. --- Mathematical optimization. --- Operations research. --- Linear and Multilinear Algebras, Matrix Theory. --- Game Theory, Economics, Social and Behav. Sciences. --- Optimization. --- Operations Research/Decision Theory. --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Combinatorics --- Algebra --- Algorism --- Arithmetic --- Math --- Science --- Foundations --- Algebra. --- Game theory. --- Decision making. --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management --- Management decisions --- Choice (Psychology) --- Problem solving --- Games, Theory of --- Theory of games --- Mathematical models --- Mathematics --- Decision making