Equilibria in multi-party systems

This paper deals with equilibria in multi-party systems, not excluding systems with two parties. The model has a one-dimensional policy space for the positions of parties and voters. Furthermore it assumes an arbitrary continuous density of voters, voters vote for the nearest party, and parties try to maximize the number of votes. Sufficient and necessary conditions for equilibria are given, and from these conditions it is deduced that for systems with a large number of parties equilibria are rare, unless the density of voters is uniform.