The steady rise in income and wealth inequality in the last four decades, together with the evolution of a vanishing middle class, has raised concerns about potentially pernicious effects of these trends on social stability and economic growth. This paper evaluates the possibility of designing tax systems aimed at reducing income inequality and bipo-larization. Using two fundamentally different metrics, we provide a unified foundation of tax progressivity whereby, roughly, taxes are progressive if and only if they are inequality reducing; and taxes are inequality reducing if and only if they are bipolarization reducing.