Social Preorders and Tax Progressivity

Income inequality, bipolarization, and polarization more generally are critical issues that have drawn the attention of economists, policymakers, and social scientists. While related, these phenomena present important conceptual differences. This paper studies the role of nonlinear income taxation as a mechanism for income inequality reduction and depolarization. We introduce a novel and intuitive variance-sensitive axiom defined on perfectly bimodal income distributions, an axiom that serves as the basis for the definition of a social preorder, which is used as the main normative criterion for the evaluation of income distributions and encompasses various inequality and (bi)polarization measures. In an endogenous income framework, we fully characterize the conditions under which income tax schedules effectively reduce income inequality and (bi)polarization, as measured by a wide range of metrics. We show that such tax schedules are necessarily progressive and characterize subsets of tax policies that simultaneously achieve a universal reduction in inequality and (bi)polarization. These results underscore the critical role of progressive taxation in mitigating economic disparities and fostering a more balanced economic landscape.