Could an Alternative Voting System Have Stopped Trump?

Now that Donald Trump is officially the Republican nominee, it is important to take a look back at the context that allowed that once unthinkable event to occur. Over the next few months and years, plenty of blog posts, essays, peer-reviewed articles, and books will investigate the cultural and economic landscape that led to Trump’s primary victory, but one piece of the context that seems to be missing from the discussion is the primary system itself. That was not always the case.

In fact, during the primary season the alternative election system of ranked-choice voting (RCV) had quite a moment in the sun. Though the idea of implementing this voting system was not novel, something about this election had people examining it a little more closely. The way RCV works is that instead of voting for a single candidate, each voter ranks all of the candidates in order of his or her preference. If no candidate has an outright majority of first-choice votes, the candidate with the fewest first-choice votes is dropped from the ballot, and those votes are transferred to each voter’s second-choice candidate. This process continues until one candidate has amassed at least 50% of the votes.

For a simple example, imagine an election between Sam, Clare, and Harry, where 40 people vote “1: Sam, 2: Clare, 3: Harry,” 35 vote “1: Clare, 2: Harry, 3: Sam,” and 25 vote “1: Harry, 2: Clare, 3: Sam.” Under the current system, Sam would win with 40% of the vote, compared to Clare’s 35% and Harry’s 25%. But under RCV, since no candidate had 50%, the person with the fewest first choice votes (Harry) would be eliminated, and his voters would be reassigned to their second choice. In this example, all 25 of Harry’s voters had Clare as their second choice, so their votes would all go to her. After this reassignment, Clare would have 60 votes to Sam’s 40, and would win with a 60% majority. Essentially, the system ensures that a candidate does not win with a plurality when the majority of voters would prefer another candidate.

If this sounds familiar, it’s probably because at the peak of the #nevertrump movement it became quite popular to discuss its merits (and the merits of similar systems). The common theory at the time seemed to be that Trump carried the first round of primaries with a plurality of 30–40% of the vote, in spite of the 60-70% of “anti-Trump” voters who would have surely united around another candidate if the field hadn’t been so split. In this telling, ranked choice voting was the white knight that could have come to the party’s rescue, offering a way to keep the nomination in the hands of the people while making sure that the eventual nominee was acceptable to the majority of voters.

While it is a compelling story, and one that is strengthened by the fact that Trump ended up with only 46% of the popular vote in the primary, it is still necessary to ask the question: Would RCV have actually changed anything? I set out to find the answer with the help of two early polls (Public Policy Polling and NBC News|Survey Monkey) that asked voters for their second-choice candidates.

Using the data from these polls as well as the number of votes cast for each candidate in each primary, I was able to simulate what might have happened in the first 15 Republican primaries and caucuses under a ranked-choice voting system. Simulations were done up to and including the Super Tuesday primaries, since the rest would require extreme guesswork about how the early primary results might have affected later candidate dropouts and voter preferences. Each state’s election was simulated 1000 times, with random noise added to account for the uncertainty in the polling data that was used (more detailed methods can be found here).

Interestingly, the results of these simulations paint a slightly more understated picture than the one often theorized. Specifically, in almost every state up to Super Tuesday the candidate who won the plurality under the current system would have been the most likely candidate to win a majority of the vote under the RCV system. The two exceptions are Arkansas, where Cruz won 77% of simulated RCV elections, and Virginia, where Rubio won 60% of simulated RCV elections, in spite of Trump winning both states under the current system.

However, the results do demonstrate that the scenario that played out for Trump under the current system was the best outcome he could have hoped for under RCV. The only states Trump had at least a 10% chance of winning under RCV were the states that he won under the current system. Compare this to the non-Trump candidates (the combination of Cruz and Rubio), who together had a very good (>50%) chance of taking two new states from Trump (Arkansas and Virginia), and a reasonable (>20%) chance of taking two others (New Hampshire and South Carolina).

Additionally, by examining all of the possible combinations of state wins and losses, it becomes clear that Trump would have been at least slightly hurt by this system. In fact, he would have had only a 7.5% chance of winning at least ten states (the number he won under the current system), compared to a 27% chance of winning nine, a 40% chance of winning eight, and a 21% chance of winning seven. By the same metric both Cruz and Rubio would have benefited slightly, each with a most likely outcome of +1 victory.

Based on these results, an interesting, though more subjective, task is the analysis of what effect such an outcome would have had on the remainder of the primaries. It is easy to imagine an 8/15 performance appearing less dominant than a 10/15 performance, especially in the early stages of the primary when Trump’s campaign was heavily focused on the idea of always “winning.” Yet at the same time, it is conceivable that 8 majority victories could have actually been more impressive than 10 plurality victories.

So although these results point in the general direction of consolidation against Trump, they are not as definitive as some would have believed. In the end, this may simply boil down to a disconnect between the degree to which journalists and politicians disliked Trump and the degree to which the Republican voters disliked Trump. While forced to acknowledge the opinions of the 30–40% of voters who voted for him, in the early stages many clung to the belief that although Trump was the first choice of those voters, he was surely the last choice of everyone else. In reality, this ceiling theory was likely false. Instead, Trump seems to have been a common second or third choice from the beginning, and stood to benefit almost as much from a shrinking field as any other candidate. This fact is likely the root of the modest effects of RCV on his success.

While ranked choice voting may not have drastically changed the course of this election, there are still several reasons why this voting system is deserving of attention and consideration. If nothing else, the deep insights into voters’ preferences that would have been provided by their ranking behavior may have proved invaluable for earlier and more effective mobilization of anti-Trump advocates. So although RCV’s implementation on a national stage is unlikely, we can all still do our part by writing our local pollsters and asking for second and third choice questions on their next mailer.

Your favorite 2020 hopeful would appreciate it.