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Multidimensional Almost Dominance: Child Wellbeing in Egypt


A major drawback of First Order Stochastic Dominance approach is dominance indetermination. Levy and Leshno in 2002 suggested Almost Stochastic Dominance as a remedy in the uni-dimensional case. We introduce a Generalization of Almost First and second Order Dominance (MAFOD and MASOD) to the multidimensional case with application on child wellbeing in Egypt. We perform a multidimensional (FOD) analysis on seven deprivation indicators for three age-groups of children from Egypt 2014 Demographic and Health Survey (EDHS14). This methodology allows the ordinal ranking of regions and governorates of Egypt in terms of their children wellbeing based on their probability of domination. To solve the dominance indetermination we apply MAFOD and MASOD.

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  1. The human poverty index measures deprivation in basic human development in the same dimensions as the HDI. HDI measures basic achievements in three dimensions: health, education and living standards. While the HPI measures deprivations in these three dimensions (UlHaq 2003; UNDP 1997).

  2. If dimensions are substitutes the marginal utility of one attribute decreases as the quantity of the other increases. If attributes are complements, an increase in the amount of one raises the marginal utility of the other (Njong 2010).

  3. The Bristol indicators were originally developed by a team at the University of Bristol and presented in the report “The Distribution of Child Poverty in the Developing World”. These indicators are based on the “deprivation approach” to poverty (Gordon et al. 2003).

  4. Net domination is the difference between row and column mean domination.

  5. Unpublished.

  6. Could be provided upon request.

  7. Results for the other two age-groups could be provided upon request.


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Correspondence to A. R. Zahran.

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El Sayed, T., Zahran, A.R. Multidimensional Almost Dominance: Child Wellbeing in Egypt. Soc Indic Res 136, 283–304 (2018).

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  • Stochastic dominance
  • Multidimensional poverty
  • Wellbeing indicators