The Prisoner's Dilemma Behind The Two-Party System

This weekend I was thinking about how the Republican party is in a bind due to Trump’s refusal to concede the election, with Republicans like Mitt Romney admonishing Trump’s actions, while others like Lindsey Graham vehemently stand by Trump. In casual discussion, one of my roommates asked me what I think the odds are that the Republican party splits. This division would seemingly split the party into a group of more moderate Republicans that want to go back to the pre-Trump Republican party, and a group of Trumpers who focus on pure political power and divisive politics. When contemplating this question, I realized that this might be a good example of a Prisoner’s Dilemma problem in politics.

We’ve seen the Republican party become divided in views/strategies of the two aforementioned groups, but we’ve also seen the democratic party stretching between super-progressive democratic socialists like Bernie Sanders, and more moderate democrats such as President-elect Joe Biden. In this article using Gallup poll data, the author explained that only 38% of Americans feel that the two parties do an adequate job, so a majority of people would support more parties. If both the Republican and Democratic parties split into more moderate and extreme subsets, everyone would feel better represented by their candidate of choice. I don’t believe this would happen though, because if one party splits, the other party instantly benefits from not splitting their party, and keeping a larger number in the caucus than both of the individual opposing parties, and can more-easily win a presidential election. If both parties were to split, both democrats and republicans would be better off than they are now, but if only one party split then the other will hold off and benefit from still being larger. Due to this, the parties are stuck in a dominant strategy prisoner's dilemma, where they don’t reach Pareto efficiency. To simplify, if both parties remain one they have utilities of (10,10). If they both split, they reach Pareto efficient utilities of (20,20). If one party splits but the other doesn’t, they have utilities of (5, 40), respectively.