This paper describes how to obtain a robust weighting scheme of well-being indicators to arrive at the least (highest) possible multidimensional poverty for a given population when we have a given set of pre-determined normative weights as a benchmark. In particular, we test whether the allocation of weights to each well-being dimension for assessing the poverty level of a given population are robust or whether different weighting schemes would have offered a highest (lowest) possible multidimensional poverty to that population. Identification of poor through the choice of dimension specific poverty lines and setting weights to different dimensions may lead to different poverty levels and a reversal of poverty assignments across populations. We offer a robust weighting scheme to the attributes of well-being which can equally well be applied to union, intersection or intermediate identification approaches when dealing with multidimensional indicators of poverty. We derive a robust weighting scheme for which multidimensional poverty is highest (lowest) for a given deprivation level. Moreover, different set of dimension specific poverty lines can be chosen where multidimensional poverty is driven by only a set of dimensions where poverty lines above these levels can no longer be considered in the multidimensional poverty comparisons. We illustrate our methodology through multidimensional poverty analysis in different population groups in Kenya and Canada.