Abstract
This paper studies the measurement of multidimensional well-being and deprivation when every attribute is discretely and ordinally measurable. In this context, we propose an axiom, Non-dominance, and use it together with some other standard axioms from the existing literature to characterize a class of measures of social well-being and also a class of social deprivation measures.
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Notes
- 1.
Note that the vectors \( a^{1} , \ldots ,a^{k} \) here are some achievement vectors each of which is possible for an individual and do not refer to the achievement vectors of any specific individuals in our society, and similarly for \( b^{1} , \ldots ,b^{k} \). In particular, \( k \) does not bear any relation to \( n \), the number of individuals in our society.
- 2.
It may be noted that we could have used individual \( i \)’s well-being (or “real overall achievement”), \( \sigma \left( {\mathop \sum \limits_{j = 1}^{m} \varphi_{j} (a_{ij} )} \right) \), and an appropriate well-being benchmark to classify if individual \( i \) is deprived or non-deprived. Given that an individual’s well-being is a positive transformation of her nominal overall achievement \( \sum\nolimits_{j = 1}^{m} {\varphi_{j} (a_{ij} )} \), the two classificatory methods are equivalent.
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Acknowledgements
We are grateful to a referee for helpful comments on an earlier version of the paper.
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Pattanaik, P., Xu, Y. (2019). Measuring Multidimensional Well-Being and Deprivation with Discrete Ordinal Data. In: Dasgupta, I., Mitra, M. (eds) Deprivation, Inequality and Polarization. Economic Studies in Inequality, Social Exclusion and Well-Being. Springer, Singapore. https://doi.org/10.1007/978-981-13-7944-4_1
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DOI: https://doi.org/10.1007/978-981-13-7944-4_1
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