A new decomposition of the Kakwani poverty index using ordered weighted averaging operators

In the literature of poverty, it is well known that every poverty index should be sensitive to the incidence of poverty, the intensity of poverty and to the inequality among the poo individuals. However, the inequality among the poor could be measured analyzing either the income of the poor distribution, or the gap of the poor distribution. Depending on the side we focus on, contradictory results could be obtained. This paper concentrates on the poverty measure proposed by Kakwani. We show that an ordered weighted averaging (OWA) operator is underlying in the definition of the Kakwani index. The dual decomposition of the OWA operator into a self-dual core and anti-self-dual remainder allow us to propose a decomposition for the Kakwani index in terms of incidence, intensity and inequality. Moreover, the properties inherited in the proposed decomposition allow us to obtain an inequality component that measure income inequality of the poor and gap inequality of the poor equally.