Assessing Deprivation with Ordinal Variables: Depth Sensitivity and Poverty Aversion

The challenges associated with poverty measurement within an axiomatic framework, especially with cardinal variables, have received due attention during the last four decades. However, there is a dearth of literature studying how to meaningfully assess poverty with ordinal variables, capturing the depth of deprivations. In this paper, we first propose a class of additively decomposable ordinal poverty measures and provide an axiomatic characterisation using a set of basic foundational properties. Then, in a novel effort, we introduce a set of properties operationalising prioritarianism in the form of different degrees of poverty aversion in the ordinal context, and characterise relevant subclasses. We demonstrate the efficacy of our methods using an empirical illustration studying sanitation deprivation in Bangladesh. We further develop related stochastic dominance conditions for all our characterised classes and subclasses of measures. Finally, we elucidate how our ordinal measurement framework is related to the burgeoning literature on multidimensional poverty measurement.