An Alternative Social Welfare Function Based on Theil's Entropy Measure

Chakravarty (1982) derived a Social Welfare Function based on a set of axioms conforming to widely shared views on measurement of welfare. The Social Welfare Function turned out to be a decreasing function of normatised Theil's Entropy Measure and an increasing function of the mean income. Theil's measure T as such, has a number of desirable properties and conforms to the Principle of Population Replication. The normalised measure (T/log n), however, fails to do so. By altering one of the assumptions in his set up an alternative Social Welfare Function has been derived. This Social Welfare Function is a negative transformation of Theil's measure as such, not normalised, and has some Interesting properties and Interpretations different from those of Chakravarty (1982).