The main contribution of this paper is to clarify some of the misconceptions about income polarization indices observed in the existing literature. Our analysis explores the domain of measures of polarization of the income distribution, with a specific emphasis on elucidating the importance of distinguishing between bipolarization and multipolarization measures. Additionally, we assert that a valid polarization metric must satisfy the principle of scale-invariance. Furthermore, in cases where the income distribution is categorized into relatively poor and relatively rich, a valid bipolarization measure should consistently increase when regressive transfers occur from poorer to richer individuals and when progressive transfers occur between two poorer or two richer individuals. The study identifies instances where bipolarization measures that fail to satisfy these criteria have been employed in previous research, leading to erroneous conclusions. The research also provides a succinct analysis of the challenges faced by scholars in employing Esteban and Ray’s multipolarization measure and its adapted versions. The study pinpoints errors in previously published works, particularly in those using the Median Relative Polarization measure with an additive median adjustment. Additionally, a real-world illustration is presented that depicts a declining trend of the bipolarization of income distribution in Brazil from 2001 to 2015, coinciding with a decrease in inequality during this period.