Anthony B. Atkinson discusses the measurement of inequality in income distribution, emphasizing the conceptual challenges and theoretical foundations. He argues that while measures like the Gini coefficient, variance, and coefficient of variation are widely used, they often obscure the need for a fully specified social welfare function to achieve a complete ranking of distributions. Atkinson draws parallels between inequality measurement and risk assessment in decision-making under uncertainty, highlighting the importance of concave utility functions and risk aversion. He introduces the concept of the equally distributed equivalent income (y_EDE), which allows for a more intuitive measure of inequality by comparing the income level needed to achieve the same social welfare as the current distribution. This measure is invariant to linear transformations of the utility function and provides a range between 0 (complete equality) and 1 (complete inequality). Atkinson examines various conventional measures of inequality, noting their sensitivity to different income levels and their implications for social welfare. He critiques the relative mean deviation for not being strictly concave and insensitive to transfers within the same income bracket. The coefficient of variation, Gini coefficient, and standard deviation of logarithms are found to be sensitive to transfers at different income levels, with the Gini coefficient placing more weight on middle-income transfers and the standard deviation on lower-income transfers. He also explores the implications of different degrees of inequality aversion, showing how varying the parameter ε in the social welfare function affects the ranking of distributions. Using data from Kuznets, Atkinson illustrates that the Gini coefficient and coefficient of variation suggest greater inequality in developing countries, while the standard deviation of logarithms does not support this conclusion. The equally distributed equivalent measure, when adjusted for different values of ε, provides a more nuanced view of inequality, showing that rankings can vary significantly depending on the assumed degree of inequality aversion. Atkinson concludes that conventional measures are misleading and that a direct approach to defining the properties of the social welfare function is more appropriate for accurately measuring inequality.Anthony B. Atkinson discusses the measurement of inequality in income distribution, emphasizing the conceptual challenges and theoretical foundations. He argues that while measures like the Gini coefficient, variance, and coefficient of variation are widely used, they often obscure the need for a fully specified social welfare function to achieve a complete ranking of distributions. Atkinson draws parallels between inequality measurement and risk assessment in decision-making under uncertainty, highlighting the importance of concave utility functions and risk aversion. He introduces the concept of the equally distributed equivalent income (y_EDE), which allows for a more intuitive measure of inequality by comparing the income level needed to achieve the same social welfare as the current distribution. This measure is invariant to linear transformations of the utility function and provides a range between 0 (complete equality) and 1 (complete inequality). Atkinson examines various conventional measures of inequality, noting their sensitivity to different income levels and their implications for social welfare. He critiques the relative mean deviation for not being strictly concave and insensitive to transfers within the same income bracket. The coefficient of variation, Gini coefficient, and standard deviation of logarithms are found to be sensitive to transfers at different income levels, with the Gini coefficient placing more weight on middle-income transfers and the standard deviation on lower-income transfers. He also explores the implications of different degrees of inequality aversion, showing how varying the parameter ε in the social welfare function affects the ranking of distributions. Using data from Kuznets, Atkinson illustrates that the Gini coefficient and coefficient of variation suggest greater inequality in developing countries, while the standard deviation of logarithms does not support this conclusion. The equally distributed equivalent measure, when adjusted for different values of ε, provides a more nuanced view of inequality, showing that rankings can vary significantly depending on the assumed degree of inequality aversion. Atkinson concludes that conventional measures are misleading and that a direct approach to defining the properties of the social welfare function is more appropriate for accurately measuring inequality.