Some characterizations in the inequality, poverty and polarization fields

Resumen

The study of inequality, poverty and polarization plays a decisive role in understanding the well-being of the population of a country. The way these issues are measured is important for a better understanding of what has happened as well as for the design of policies on well-being. The setting of desirable axioms or properties is a crucial step to derive indices. The aim of the first chapter of this thesis is to propose a natural generalization of the unit consistency axiom proposed by Professor Zheng in the unidimensional setting to the multidimensional setting, and then to characterize classes of multidimensional inequality and poverty measures which are unit-consistent. Chapter 2, following Zhengs proposal we explore the consequences of the unit-consistency axiom in the polarization field and propose and characterize a class of intermediate polarization orderings which is unit-consistent. In Chapter 1 we have limited the scope of the investigation to a reasonable framework of properties for multidimensional poverty measures. It may be worth noting that the families proposed by Bourguignon and Chakravarty (2003) and Alkire and Foster (2008) does not belong to the family we derive, and satisfy the unit consistency axiom. Since these families can attract a great deal of interest in the field of poverty measurement, in Chapters 3 and 4 we explore a number of properties fulfilled by these measures and then we characterize them.