U.S. congressional roll-call voting records show that as polarization of the two parties along the economic dimension changes, polarization along the social/cultural dimension tends to change in the opposite direction. A model of party competition within a two-dimensional ideology space is developed in which party platforms are determined by voters who compose the party. It is shown that if distribution of voter preferences is radially symmetric, polarization of party ideologies along the two dimensions are inversely related, as observed. The model gives a remarkably good quantitative account of the historically observed movements in polarization along the two dimensions.

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