The Stability of Four Political Parties in the U.S.
As presidential candidates rev their engines for their campaigns for the coming 2016 election, fault lines in political parties become more apparent. Last December, Philip Bump of the Washington Post published his speculations of the fate of the Democratic and Republican parties in an article entitled “What would happen if Congress split into four parties? This.” Bump wrote this article in light of the unexpectedly split votes by the Democrats in Congress on a spending bill in December 2014 . He entertains the idea of the Democratic party bifurcating over spending and following a path not unlike that which, Bump implies, the Republican party seems to be following.
We can apply our knowledge of networks to assess how stable a government with four opposing parties might be. We can make a graph with each node representing a party and each edge being the relationship between two parties. It is probably safe to assume party knows of and has a relationship with each of the other three parties, so the graph would be complete. We can then easily assess whether the graph is balanced and infer the stability of each possible network of relations.
A network in which all parties are adversaries of each other would not be balanced. (It would also make for an extremely unstable government.) If each party had exactly two allies and one rival, the network would also not be balanced. The network would be balanced if all parties had positive relationships with one another, but seems unlikely. More likely, if two unique pairs of parties were to each form an alliance, the network would also be balanced. Another example of a balanced configuration would be if three of the four parties allied and opposed the fourth party. This network of three against one would indicate that the one lone party was dominant. Bump’s article implies that two distinct alliances is the fate of the United States government, and according to our very simplified model, if no single party rises to power, that is likely how it shall remain.
Bump suggests that the alliances would be Liberals with Democrats and Conservatives with Republicans. However, recall that Bump’s speculations are based on the votes on a 2014 spending bill. To truly model the government with networks, we would need a more complex graph. We would have to take into account many more factors, including how party lines would vary based on different issues not just financial. If we assume four parties, two pairs of allies remains as the most likely and realistic configuration of party relations. But would the same pairs of parties be allies for all issues?
Needless to say, this analysis would be much simpler if all parties were united by positive relations. Then again, the more complex reality of politics should make for an exciting 2016.
Source: http://www.washingtonpost.com/news/the-fix/wp/2014/12/15/welcome-to-the-four-party-congress/