What we found is surprising: There is no clear contest between the “establishment” candidates, such as Jeb Bush or Marco Rubio, and “outsiders,” such as Donald Trump, Ben Carson or Carly Fiorina. The campaign isn’t creating polarized camps of Republican voters.
In this poll, we asked Republicans to indicate all the candidates that they would be willing to vote for in their state’s primary or caucus. We then asked them to rank these candidates.
We then created a map of the Republican field based on what we call “shared supporters.” If a voter selected both Bush and Rubio in response to the first question, those two candidates are connected by at least one shared supporter. The more supporters two candidates share in common, the stronger the connection (or tie) between those candidates. This is represented in the graph below by wider and darker lines.
We also wanted to capture only higher levels of shared support, so the graph below includes ties between candidates only if their number of shared supporters is higher than the overall average. The circles representing candidates are larger or smaller depending on how many voters were willing to vote for them.
There are several notable findings. Perhaps unsurprisingly, Jim Gilmore, Lindsey Graham, and George Pataki don’t even appear, meaning that they do not share ties with any other candidates. So few voters were willing to vote for them that they did not even qualify to be depicted here.
Second, the graph shows that all of the front-runners — Trump, Carson, Ted Cruz, and Rubio — share lots of supporters. Many voters are just as willing to support any of these candidates as they are to support their current top choice. The campaign has not been particularly polarizing thus far.
Third, we do not find two clear clusters of “outsider” candidates and “establishment” candidates. We might expect Trump, Carson and Fiorina to have the same base of voters, while Bush and Rubio would have a different base of voters.
But this pattern isn’t evident at all. For example, Rubio shares many supporters with “outsiders” like Trump, Carson and Fiorina. In fact, Rubio actually looks like the bridge between “establishment” candidates, such as Bush and Chris Christie, and “outsider” candidates, such as Trump, Carson and Fiorina.
We also measured each candidate’s “connectedness” in the network. This captures who is linked to the most candidates and therefore has the most to gain as others drop out of the race. Rubio, Carson and Fiorina were tied on this measure. They are thus well positioned to pick up supporters from candidates who may drop out.
Another interesting question is where a candidate’s supporters would go next once he or she exits the race. We can examine this question because we know not only each voter’s first choice but also their second choice.
We created a second graph that depicts how many voters would move from one candidate to another if their first choice dropped out. In this graph, darker arrows indicate that more supporters would shift from one candidate to the other. For example, more of Trump’s supporters would move to Cruz or Carson than to Rubio or Bush.
Carson, Cruz, Trump, and Rubio are all tied together in the center of the plot. If any one of them were to drop out, most of their supporters would shift to another of the front-runners.
But Cruz seems particularly well positioned to pick up support if both Carson and Trump exit. Many Carson and Trump supporters list Cruz as their second choice.
Rubio, on the other hand, stands to gain a significant number of supporters if Carson’s campaign ends, but fewer if Trump drops out.
There are also some interesting ties that do not exist. This is most notable for Trump. As the front-runner in our poll, he has the most first-place support, but he still was not the first choice for 70 percent of Republican voters.
What’s striking in the graph is how few arrows run to Trump. In fact, the exits of only two candidates — Carson and Cruz — are likely to benefit Trump. No other candidate’s supporters list Trump as a second choice.
This suggests a potential ceiling on Trump’s support, at least for a while. Unless the candidates who drop out are Carson or Cruz, Trump won’t immediately benefit.
Of course, these results derive from a single national survey that only provides a snapshot of the race. If the polls shift, so would the relationships we’ve captured.
But in this crowded field, understanding voters’ second choices paints a more nuanced portrait of the race.
Mia Costa is a Ph.D. candidate in political science at the University of Massachusetts-Amherst. Brian Schaffner and Ray LaRaja are professors of political science at the University of Massachusetts-Amherst.