Welfare judgements on distribution of income has often been made on the basis of weighted sum of individual incomes. Scholars proposed various axioms to determine the weights. The set of weights proposed by Chakrabarty (1982) led to a Social welfare function (SWF) involving the normalised Theil’s Entropy Measure. We have proposed a few alternative sets of weights here which lead to SWFs involving the Theil’s measure as such and a new measure of inequality. An alternative formulation leads to another pair of SWFs involving the Variance of Income Power. These SWFs are seen to have certain interesting properties and interpretations.