A Reduced Posetic Approach to the Measurement of Multidimensional Ordinal Deprivation

In this paper, we discuss the existence of particular systems of generators for posets associated to multidimensional systems of ordinal indicators and derive a reduced posetic procedure for the measurement of multidimensional ordinal deprivation. The proposal is motivated by the need to lessen the computational complexity of the original posetic procedure described in Fattore (Soc Indic Res 128(2):835–858, 2015), so as to make it applicable to larger multi-indicator systems, particularly to those comprising many variables scored on “short” scales, as typical in deprivation studies. The reduced procedure computes identification and severity functions based only on so-called lexicographic linear extensions. These are a particular generating system for the basic achievement poset, naturally associated to rankings of deprivation attributes. After motivating this choice, both from an interpretative and a computational point of view, the paper provides some simulated examples, comparing the reduced and the non-reduced procedures.