In this book we are concerned with income profile based ethical social index numbers. An ethical index is designed from an explicit social evaluation function with a specific purpose in mind. For example, an ethical relative inequality index determines the fraction of total income that could be saved without any welfare loss if society distri- buted incomes equally. Ethical indices contrast with descriptive indices which are de- rived without using any concept of social welfare. Needless to say, ethical indices are not meant to supplant descriptive indices, rather they are constructed with different aims. We begin Chapter 1 with a formal discussion on the concept of a social evaluation function. In the main body of this chapter we consider the problem of ranking income profiles using a social evaluation function. In Chapter 2 we set about analyzing alter- native approaches to the measurement of inequality. In Chapter 3 we focus our attention on the Gini index, the most frequently used index of inequality, and its extensions. In Chapter 4 we formulate the notion of an ethical distance function that measures welfare of one population relative to another. Chapter 5 is devoted to quantifications and discussions of alternative definitions of relative deprivation put forward by Runci- man(1966).
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