Ethical Social Index Numbers

The subject of this book is income distribution based social index numbers. These index numbers quantify different aspects of income distribution data. The topics covered are: inequality, economic distance, relative de- privation, poverty, tax progressivity, horizontal inequity and mobility. The main purpose of the book is to present the significant results on welfare theoretic ap- proaches to income distribution based measurement problems. Discussions of descriptive approaches, which do not make use of a concept of social welfare, are also included. Thus the book gives an overall view of the recent developments in this subject. The technical terms and mathematical operations employed to discuss the results are explained in nontechnical terms, and intuitive explanation of the mathematical results are given. Numerical illustrations of some of the results are provided using income distribution data.

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).

This book gives an overall view of the application of social evaluation functions to various income distribution based measurement problems. Many of the results presented are applicable to attributes other than income. The book will be useful for economists, political theorists, sociologists, statisticians and others.