<p>This paper addresses and clarifies key misconceptions surrounding income polarization indices commonly observed in the literature. It focuses on the measurement of the polarization of income distributions, emphasizing the crucial distinction between bipolarization and multipolarization measures. The analysis asserts that valid polarization metrics must satisfy the principle of scale invariance. Specifically, in a dichotomized income distribution (relatively poor vs. relatively rich), a valid bipolarization measure should consistently increase under regressive transfers from poorer to richer individuals or progressive transfers within either income group. The study identifies cases where bipolarization measures that fail to satisfy these conditions have been applied in previous research, leading to erroneous conclusions. Using artificial numerical examples, the paper demonstrates the behavior of different polarization measures under various scenarios, illustrating their limitations. The study concludes by highlighting errors in previously published works and offering a critical reassessment of established methodologies.</p>