Hotelling’s Model of Spatial Competition shows that in a linear world two businesses of the same type will locate next to one another. This way each business will be closest to and therefore, get business from 50% of the customers. 

While this model helps explain business locations we do not live on a line and there are frequently more than two businesses of the same type. This does, however, quite accurately describe the political situation in the United States.

Since there are only two parties, political belief has been squeezed into a linear model with each party taking its post next to the other in the middle of this artificial line to get as many votes as possible. There are, however, at a minimum two axis to political belief, social and fiscal.

What happens if a third party, powerful enough to compete with the existing parties, is introduced? Three parties cannot all locate in the middle of a linear world and gain access to the same number of votes, so the existing equilibrium would be removed. It may even force the parties to accept that political belief is not linear and get them to compete on multiple axis.