The Democratic Primaries and The Prisoner’s Dilemma: Why Moderates Dropped Out
In the realm of electoral politics, the phenomenon of vote splitting occurs when candidates competing to represent the same political majority split the population’s votes and inadvertently increase the chances of victory for a candidate belonging to an opposing party. While this type of situation may play itself out just like it is described above, there are many circumstantial nuances that can cause vote splitting to play out in different ways. For example, in the recent California Gubernatorial Recall Election, incumbent Democratic Governor Gavin Newsom faced the possibility of being outed from office as a result of the voting format: voters were asked to vote “yes” or “no” on the recall, and then select a candidate to replace Newsom in the event of the recall. In this election’s case, the opposing Republican party tended to vote “yes” on the recall, but their many choices for Newsom’s replacements were split in popularity. One of these Republican candidates, in the chance that more than 50 percent of voters chose to recall Newsom, would replace him, despite the fact that this candidate would likely have significantly less popular support than Newsom. Another such tangential application of vote splitting occurred in the Democratic Primaries for the 2020 Presidential Election, in which a large number of moderate candidates with split popularities decided to drop out of the race on the brink of Super Tuesday, and publicly throw their support behind the marginally more popular moderate candidate and ultimate election winner Joe Biden.
The situation engulfing these Democratic candidates and their choice to drop out of the election was described by David Byler—a data analyst and columnist for the Washington Post—as a solved prisoners’ dilemma in his Opinion article published immediately after Super Tuesday. The way Byler frames it, the sheer magnitude of moderate Democratic candidates (Tom Steyer, Amy Klobuchar, Pete Buttigieg, as the more relevant examples) split up the moderate vote, thus pushing the most popular progressive candidate, Bernie Sanders, to the lead, despite the fact that all of these moderates were reaching for the opportunity to defeat Sanders in the primaries (since they believe that if Sanders was nominated as the Democratic candidate, his lack of “electability” would ensure another Trump term). However, by dropping out of the race right before Super Tuesday and throwing their support behind Biden—whether that be to prevent future monetary losses, integrate themselves into Biden’s future presidential campaign, or simply increase Biden’s following—had the effect of various moderate voters ultimately shifting their support towards the ex-Vice President and pushing him ahead of Bernie Sanders. The situation can be represented via a prisoners’ dilemma in the sense that the moderates needed to collaborate and abandon their individual goals of winning the primary for the larger goal of allowing Biden, seen as the most “electable” candidate by many, to ultimately represent the Democratic party.
While the article articulates the concept of a prisoners’ dilemma and applies it to this political situation, it is possible to communicate the candidate’s circumstances and strategic mathematically, using a concrete game theory pay-off matrix. Thus, the process of the 2020 Democratic Primaries, and the question over why only somewhat popular moderates stayed in the race for so long, can be expressed using a standard matrix depicting the pay-offs akin to those in a prisoner’s dilemma. For the sake of simplicity, the game is represented as a non-repeated, discrete game, in which there will be two players: both are two active moderate Democratic candidates at a time prior to Super Tuesday. It is assumed that the players are the two main competitors for the spot, but in reality of course there were several candidates competing for the moderate vote. Say we choose Pete Buttigieg and Joe Biden as our representatives for this game:
Whether the players both stayed or both dropped out, the end result is essentially the same: Sanders would win the nomination, and, according to moderates, would struggle with electability and proceed to lose to Trump. The players both finish with very low pay-offs. The only difference is dropping out early would save some of the player’s campaign money, which is why (Drop Out, Drop Out) carries slightly higher pay-offs than (Stay, Stay). If one player drops out and the other stays, the latter receives the highest pay-off possible: winning the nomination and potentially the general election. The Nash Equilibrium, or the state where neither player would be better off pursuing another strategy, of the game thus lands on (-7, -7), in which both candidates continue to fight for the Democratic nomination. When this process is viewed as a simple competition between two moderate candidates, the matrix helps explain why top contestants were reluctant to drop out of the race: in an overwhelming urge to follow self-interest, the candidates trapped themselves into a situation with the lowest combined pay-offs.
Although this model remained accurate for a significant portion of the primary campaign season, a large number of major moderate candidates began dropping out right before Super Tuesday—such as Steyer, Klobuchar, and Buttigieg—and Elizabeth Warren and Michael Bloomberg followed shortly after the event. While Warren and Bloomberg likely set Super Tuesday as the deciding marker for the direction of their campaign ahead of time, the explanation to why Buttigieg and Klobuchar dropped out less than a day before March 3rd may lie in the changing preferences of the candidates; perhaps the fear of Sanders as the Democratic nominee decreased their willingness to take a chance on a higher pay-off.
Recognizing Biden’s marginal lead over other moderate candidates, Buttigieg and Klobuchar would thus strategically drop out right before Super Tuesday and publicly throw their support behind Biden. They possibly had the intention of merging their followers under one candidate right before several primary elections allotting many delegates, giving Democrats a greater shot at the election, which ultimately does result in a relatively high pay-off for any moderate, whether they dropped out or made it.
Referenced Article: https://www.washingtonpost.com/opinions/2020/03/04/real-winner-super-tuesday-is-democratic-party-itself/