Methodology and Axiomatic Characterization of a Multidimensional and Fuzzy Measure of Deprivation
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Methodology and Axiomatic Characterization of a Multidimensional and Fuzzy Measure of Deprivation Dipesh Gangopadhyay1,2 · Robert B. Nielsen1,3 · Velma Zahirovic‑Herbert1,4 Accepted: 3 September 2020 © Springer Nature B.V. 2020
Abstract This article proposes a general methodology to measure multidimensional deprivation in a fuzzy setup. Each dimension comprises multiple dimensional attributes. The methodol‑ ogy is developed in a flexible manner to incorporate any theoretical construct of wellbeing. The new fuzzy membership functions proposed in the method combines the absolute and relative notions of deprivation and take the functional form of normalized and weighted deprivation gaps. A new weight structure is proposed for aggregations within and across the dimensions. Three forms of deprivation indices are discussed: the headcount ratio, the adjusted deprivation index, and the deprivation index. A unified axiomatic framework is discussed for the multidimensional and fuzzy measures of deprivation. Various desired axi‑ omatic properties of the fuzzy membership functions are included as precursory axioms in the framework. The proposed measure satisfies a majority of the desirable axioms. Keywords Deprivation measure · Multidimensional · Absolute and relative · Fuzzy · Distribution sensitive · Axioms JEL Classification C18 · C43 · D63 · I30 · I32
* Dipesh Gangopadhyay [email protected] Robert B. Nielsen [email protected] Velma Zahirovic‑Herbert [email protected] 1
Department of Financial Planning, Housing, and Consumer Economics, University of Georgia, 213 Dawson Hall, 305 Sanford Dr., Athens, GA 30602, USA
2
Present Address: Data Quality Assurance Division, National Statistical Office, Government of India, Mahalanobis Bhavan, 164 G. L. T. Road, Kolkata 700108, India
3
Present Address: Department of Consumer Sciences, The University of Alabama, 316 Adams Hall, Box 870158, Tuscaloosa, AL 35487, USA
4
Present Address: Department of Financial Planning, Housing, and Consumer Economics, UGA Griffin Campus 1109 Experiment Street, Griffin, GA 30223, USA
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1 Introduction Over the past several decades, there has been a paradigm shift in the scholarship on pov‑ erty with three fundamental debates gaining prominence. First, several scholars observed limitations in the traditional money metric evaluation of poverty in terms of income or consumption and championed the idea of multidimensional measurement in terms of both income and non-income dimensions of deprivation, as a more justified and comprehensive form of evaluation of poverty. Second, the scholars have accepted poverty as a fuzzy con‑ cept and found it more appropriate to consider the presence of varying degrees of poverty among the population rather than an arbitrary dichotomization of poor and non-poor peo‑ ple based on a poverty line. Third, as the ideas of inequality, social participation, inclusion, and social justice are gaining prominence in the parlance of development economics, there has b
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