AbstractThe growing polarization of our societies and economies has been extensively studied in various disciplines and is subject to public controversy. Yet, measuring polarization is hampered by the discrepancy between how polarization is conceptualized and measured. For instance, the notion of group, especially groups that are identified based on similarities between individuals, is key to conceptualizing polarization but is usually neglected when measuring polarization. To address the issue, this paper presents a new polarization measurement based on a grouping method called “Equal Size Binary Grouping” (ESBG) for both uni- and multi-dimensional discrete data, which satisfies a range of desired properties. Inspired by techniques of clustering, ESBG divides the population into two groups of equal sizes based on similarities between individuals, while overcoming certain theoretical and practical problems afflicting other grouping methods, such as discontinuity and contradiction of reasoning. Our new polarization measurement and the grouping method are illustrated by applying them to a two-dimensional synthetic data set. By means of a so-called “squeezing-and-moving” framework, we show that our measurement is closely related to bipolarization and could help stimulate further empirical research.
Expressing Two-Dimensional Discrete Data Algebraically by Using 2D-FFT Components