Bentham (1789) introduced utility as the pursuit of happiness, with happiness defined in his philosophical view as existing if “pleasure” predominated over “pain.” This paper is the first to derive and compare the relative frequency distributions of income and utility in Bentham’s classical sense. A utility-based Gini coefficient is formulated from a utility distribution derived from the better known income distribution. A utility-based Lorenz curve is defined as the accumulated sum of pain and pleasure, as Bentham defined them. A utility-based polarization index is created as the ratio of accumulated pain to accumulated pleasure. If raw income data are unavailable, an income distribution can still be estimated from a summary inequality statistic such as the Gini coefficient using the maximum entropy method. In this study, a measure of true income inequality, utility inequality, and the “pain” suffered by the poorest group are quantified and estimated using National Tax Service data from Korea.
Gini coefficient; maximum entropy method; utility Gini coefficient; utility Lorenz curve; utility polarization index.