  The median-voter hypothesis predicts convergence of party platforms across a
one-dimensional political spectrum during majoritarian elections. Assuming that
the convergence is reflected in legislative activity, we study the time
evolution of political polarization in the National Assembly of the Republic of
Korea for the past 70 years. By projecting the correlation of lawmakers onto
the first principal axis, we observe a high degree of polarization from the
early 1960's to the late 1980's before democratization. As predicted by the
hypothesis, it showed a sharp decrease when party politics were revived in
1987. Since then, the political landscape has become more and more
multi-dimensional under the action of party politics, which invalidates the
assumption behind the hypothesis. For comparison, we also analyze
co-sponsorship in the United States House of Representatives from 1979 to 2020,
whose correlation matrix has been constantly high-dimensional throughout the
observation period. Our analysis suggests a pattern of polarization evolving
with democratic development, from which we can argue the power and the
limitation of the median-voter hypothesis as an explanation of real politics.
