Decomposition of Normalization Axiom in the Measurement of Poverty
In the measurement of poverty, Sen (1976) proposed the "normalization axiom" which has been used as the basis for deriving several alternative measures of poverty including that of Sen (Anand 1977, Kakwani 1980 and Clark, Hemming and Ulph 1981). In a recent note, Basu (1985) provided an axiomatic justification of the "normalization axiom" by means of three elementary axioms. He demonstrated that these three axioms are equivalent to Sen's normalization axiom. The purpose of the present note is to demonstrate that the theorem proved by Basu is incorrect, i.e., the three axioms proposed by him are insufficient to derive the normalization axiom. The present note also comments on Sen's measure and proposes an alternative measure of poverty which, in some respect, is more desirable than that of Sen.