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Ranking Karnataka Districts by the Multidimensional Poverty Index (MPI) and by Applying Simple Elements of Partial Order Theory

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Abstract

This study focuses on the Multidimensional Poverty Index (MPI) ranking. The standard ranking process of the MPI produces a single total (linear) rank of units by simply ordering them from the best to the worst (or the inverse) as a function of their MPI score. However, units are not necessarily comparable regarding all 10 indicators simultaneously on which the MPI is based. We use the 2012/13 India District Level Household Survey wave four with a special focus on the State of Karnataka. By using partial order theory (i.e. the Hasse Diagram technique and the software package PyHasse), we found that, in Karnataka, the number of incomparabilities greatly exceeds the number of comparabilities. This indicates that the aggregation process leading to the MPI hides the individual role of indicators. We utilized a number of tools in partial order theory to analyze the comparabilities and incomparabilities. This included local partial order, antichain, and average height analysis. In contrast with the standard MPI ranking, partial order theory provides average height which does not only account for comparable districts, but also considers to what extent incomparable districts influence the position of a district in the ranking. We found that the results of partial order ranking deviate considerably from those of the MPI ranking. Given the extent of incomparabilities, for most of our sample, the MPI ranking does not provide an adequate ranking. The Hasse Diagram technique, can therefore be seen as a synthetic ranking tool or a robustness tool that complements the standard ranking process of the MPI.

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Notes

  1. We note that different weights distribution can modify the MPI and the derived ranking. Therefore, the posetic approach, being independent of weights seems to be particularly useful.

  2. Generally, the number of poor is denoted by q (see UNDP 2015, p. 9). However, in order to avoid confusion with the notations of partial order theory, we prefer to use p for mentioning the poor in the Sect. 2.3.1.

  3. MPI is the sum of weighted censored headcount ratios regarding each indicator.

  4. The term censored means that the calculations of headcount ratio includes only the multidimensionally poor population.

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Acknowledgements

This contribution is based on the project ‘Multidimensional well-being: conceptual, methodological, analytical perspectives’, financed by the Indo-Swiss Joint Research Programme in the Social Sciences (seed money grants). We also thank the Ministry of Health and Family Welfare, India for providing us the data.

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Authors and Affiliations

  1. Department of Sociology, University of Neuchâtel, Faubourg de l’Hôpital 27, 2000, Neuchâtel, Switzerland

    Tugce Beycan & Christian Suter

  2. Institute for Social and Economic Change, Dr. V.K.R.V. Rao Road, Nagarabhavi, Bengaluru, India

    B. P. Vani

  3. Department Ecohydrology, Leibniz-Institute of Freshwater Ecology and Inland Fisheries, Müggelseedamm 310, Berlin, Germany

    Rainer Bruggemann

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  1. Tugce Beycan
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  2. B. P. Vani
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Correspondence to Tugce Beycan.

Appendix

Appendix

See Tables 7 and 8.

Table 7 Weighted censored headcount ratios per indicator and the aggregated MPI score (in %) for each district of Karnataka, with SC (years of schooling), CE (child enrolled), CM (child mortality), NU (nutrition), EL (electricity), SA (toilet), DW (drinking water), FL (floor), CF (cooking fuel), AS (assets)
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Table 8 Incomparability among the maximal elements due to the Hasse Diagram (see Fig. 2)
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Beycan, T., Vani, B.P., Bruggemann, R. et al. Ranking Karnataka Districts by the Multidimensional Poverty Index (MPI) and by Applying Simple Elements of Partial Order Theory. Soc Indic Res 143, 173–200 (2019). https://doi.org/10.1007/s11205-018-1966-4

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