Poverty measurement with ordinal variables: A generalization of a recent contribution

Bennett and Hatzimasoura (2011) derive a new class of poverty measures suitable for ordinal variables. These indices are weighted sums of the population probabilities of attaining each state of the ordinal variable which is below the poverty line. The weights are uniquely determined by the choice of the classi?single parameter and by the number of ordinal states below the poverty line. However, as I show in this note, such restrictive propery is not necessary for the derivation of poverty measures for ordinal variables that satisfy a broad array of desirable properties, including those advocated by Bennett and Hatzimasoura. The class of measures proposed in this note include those of the authors, as a specific subclass. Since the class of admissible poverty measures for ordinal variables is unbounded, the note provides two dominance conditions whose fulfillment ensure the agreement of ordinal poverty comparisons among measures belonging to subfamilies within the class.