A Spatial Voting Model Where Proportional Rule Leads to Two-Party Equilibria
n this paper we show that in a simple spatial model where the government is chosen under strict proportional rule, if the outcome function is a linear combination of parties' positions, with coefficient equal to their share of votes, essentially only a two-party equilibrium exists. The two parties taking a positive number of votes are the two extremist ones. Applications of this result include an extension of the well-known Alesina and Rosenthal model of divided government as well as a modified version of Besley and Coate's model of representative democracy. Different outcome functions are then analyzed.
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