Symmetric Nash equilibrium of political polarization in a two-party system

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