A well‐established strategy for evaluating alternative income distributions is based on the use of an abbreviated social welfare function that depends only on mean income and an inequality index. In keeping with this literature, we study the existence of social welfare functions that can be written as a trade‐off between efficiency and income polarization. This paper proposes a class of social welfare functions consistent with the Esteban and Ray, and Duclos, Esteban and Ray income polarization indices. For this result, we expand the domain for personal preferences to incorporate not only own income but also the well‐being of others. In addition, we link our proposal to the literature on relative satisfaction. The approach is illustrated by an empirical application using the CPS database for the United States in the period 1991–2010.