An intra-group variance based polarization measure

In this paper, it will be shown that polarization not only depends on identification and alienation. There exist additional factors such as the share of power held by each of the groups and the number of groups that should be considered to compute it. Consistent with this idea and with the basic principles of polarization of Esteban and Ray (1994), we define a measure of polarization as the product of three factors: the alienation-identification, the share of power of the groups and the number groups. The first factor is defined following an identification-alienation framework based on the decomposition of the variance. This differs from the expression defined by Esteban and Ray (1994) and Zhang and Kanbur (2001). The second factor values the importance of the middle class as a factor of social stability. This factor, jointly with the third, extends and corrects the approach to polarization of Zhang and Kanbur (2001). A comparison of the defined measure is made with the main expressions existing in the studies about income polarization. For this, data derived from the ECHP (1994-2001) for Spanish Households are utilized.