  The median-voter hypothesis (MVH) predicts convergence of two party platforms
across a one-dimensional political spectrum during majoritarian elections. From
the viewpoint of the MVH, an explanation of polarization is that each election
has a different median voter so that a party cannot please all the median
voters at the same time. We consider two parties competing to win voters along
a one-dimensional spectrum and assume that each party nominates one candidate
out of two in the primary election, for which the electorates represent only
one side of the whole population. We argue that all the four candidates will
come to the same distance from the median of the total population through
best-response dynamics.
