The multidimensional extension of the Aleskerov-Golubenko polarization index is developed. Several versions of the polarization index are proposed based on different distance functions. Basic properties of the index are examined. The behavior of polarization index is studied numerically in the case of the “uniform” distribution of groups in the unit square and unit three-dimensional cube. Polarization in the Russian State Duma (1994–2003) is studied using the index elaborated. The two-dimensional model of the Russian State Duma previously developed on the basis of publically available roll-call data is 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.
