Marco Fattore

Poverty is a fuzzy and complex phenomenon which is intrinsically multidimensional. First attempts of tackling poverty with multidimensional measures trace back to the seventies with the conceptual writings on income poverty by Amartya Sen (1976). Since then much research has been devoted to answer questions of the type: (i) Who is poor? (ii) How poor is a poor? The measure of poverty and social exclusion is certainly a key point in poverty description. While much effort has been put in the last decades to the measurement of poverty, less attention has been paid to find relations among different poverty aspects. In this paper, we start from a classical definition of the population of the poor and we employ Fuzzy Multi-Criteria Analysis to provide an attempt to relate poverty aspects to one another, which we call a ‘structural representation of poverty’. Our focus is on the pattern of implications existing among different descriptors characterizing poverty aspects. We show how fuzzy relation theory and partially ordered set techniques are effective in representing complex relational structures and provide new insights into multidimensional poverty. As simple test cases the method is applied to data concerning two Italian regions based on EU-SILC database 2004. Keywords: Multidimensional Poverty, Multi-criteria Analysis, Poverty Structure, Ordinal Variables, Posets, Fuzzy Quasi-order Relations.

The evaluation of material deprivation, quality of life and well-being very often requires to deal with multidimensional systems of ordinal variables, rather than with classical numerical datasets. This poses new statistical and methodological challenges, since classical evaluation tools are not designed to deal with this kind of data. The mainstream evaluation methodologies generally follow a counting approach, as in a recent proposal by Alkire and Foster pertaining to the evaluation of multidimensional poverty. Counting procedures are inspired by the composite indicator approach and share similar drawbacks with it, computing aggregated indicators that may be poorly reliable. A recent and alternative proposal is to address the ordinal evaluation problem through partial order theory which provides tools that prove more consistent with the discrete nature of the data. The goal of the present paper is thus to introduce the two proposals, showing how the evaluation methodology based on partial order theory can be integrated in the counting approach of Alkire and Foster. Keywords: Partial Order theory, Counting Approach, Evaluation, Material Deprivation, Quality of Life