Multidimensional Polarization Index and its Application

The multidimensional polarization index was developed and applied to the cases of the Russian State Duma (1994 – 2003) and the U.S. House of Representatives (1879 – 2015). The following objectives were set in the work: to develop a multidimensional model of a society and a multidimensional polarization index within this model, to examine the properties of the index suggested, and to to apply it to real data. The multidimensional polarization index was developed on the basis of the first central moment of a system of forces. Several versions of index were suggested based on different distance functions. Basic properties were examined of polarization index elaborated. The behavior of polarization index was studied numerically in the case of the «uniform» distribution of groups in the unit square and unit three-dimensional cube. The two-dimensional model of the State Duma (1994 – 2003) previously developed on the basis of publically available roll-call data was used in the analysis. The results of application of the multidimensional index are consistent with occurring political events. It is shown that polarization in the State Duma was mostly associated with the degree of tension in its relations with the executive authorities. Particularly, the more severe was the confrontation between the legislative and the executive branches of power, the less polarized was the State Duma, and vice versa. In the analysis of the U.S. House of Representatives (1879 – 2015) two-dimensional DW-NOMATE scores were used. According to the results obtained, the U.S. House of Representatives was the least polarized during the period from 1930s to 1970s and the most polarized in the last available for the analysis 113th U.S. Congress (2011 – 2015). As expected, polarization in the U.S. House of Representatives from 1994 to 2003 was less than polarization in the Russian State Duma during the same period.