A cartogram illustrates the results of the 2016 presidential election by county, with red, blue, and purple to indicate voting percentages, but skewed to represent population. (Images: SFI External Professor Mark Newman)


Media in the U.S. have already been covering the lead-up to the 2020 U.S. presidential election for months, and in the years since the 2016 election, researchers at SFI have been taking a complex systems approach to understanding the political landscapes in the U.S. and around the world. As we enter this election season in earnest, here are some of the highlights of our election-related science, from new ways to illustrate political maps to different polling questions for better predictions.


In 2016, SFI External Professor Mark Newman (University of Michigan) developed a variety of election cartograms that play with scale, representing counties and states proportionally based on their populations or representation in the electoral college. These graphical representations offer a fresh perspective on the political landscape in the U.S. by combating the “apparent paradox” of the traditional, geographically proportional red-and-blue map. This paradox, Newman notes on his website, “fails to allow for the fact that the population of the red states is on average significantly lower than that of the blue ones. The blue may be small in area, but they represent a large number of voters, which is what matters in an election.”


We usually rely on polling to predict election outcomes, but those polls are not always reliable; in the 2016 U.S. presidential election, Hillary Clinton lost in five states where polls had anticipated her victory. In a February 2018 paper published in Nature Human Behaviour, SFI Professor Mirta Galesic and co-authors examined an alternative approach. Whereas most election polls ask people about their own voting habits, Galesic and her colleagues found that questions about the views of a voter’s social circle actually provide more insight, improving the accuracy of voting predictions. The researchers studied the usefulness of social-circle questions in both the 2016 U.S. presidential election and the 2017 French presidential election by means of national pre-election surveys and aggregate polls. The results indicate the efficacy of social-circle questions in tapping into ‘local’ wisdom rather than asking potential voters to make assumptions about the behavior of the general population.

Read the paper at doi.org/10.1038/s41562-018-0302-y


In the May/June 2019 Comptes Rendus Physique, SFI Professor Sidney Redner offered a minireview of the voter model that has played a central role in both probability theory and statistical physics. The classic voter model, which randomly selects a voter who then adopts the state (voting habits) of a neighbor, lacks nuance, resulting in consensus that is not always achieved in reality. In his review, Redner presented a variety of extensions to this model that endeavor to incorporate socially motivated aspects of decision making. A lack of corresponding empirical data means we should avoid mistaking these extensions for social reality, but they provide useful descriptions of how opinions can change over time in large-scale populations.

Read the paper at doi.org/10.1016/j.crhy.2019.05.004


The U.S. isn’t the only country concerned with voter fraud. The results of Turkey’s 2017 constitutional referendum indicated majority support of the country’s shift to autocracy, but allegations of electoral irregularities and misconduct suggest otherwise. In a 2018 PLOS One paper, SFI External Professor Stefan Thurner (Complexity Hub Vienna) and his collaborators applied statistical forensics tests to identify and verify cases of malfeasance. They utilized  election data made available on the election commission’s website, removing potential outliers and examining election fingerprints. The researchers found “systematic and highly significant statistical support for the presence of both ballot stuffing and voter rigging.” These statistical irregularities persisted in the 2018 presidential and parliamentary elections, indicating systematic biases that need to be combated.

Read the paper at doi.org/10.1371/journal.pone.0204975


History offers up numerous examples of near 50-50 election results. In the past decade alone, we’ve witnessed the 2014 Swiss referendum on mass immigration, the 2016 U.S. presidential election, and the British Brexit vote (also in 2016). All three were characterized by controversial issues and hostile attacks on both sides, and all three ended in a near stalemate, with a narrow margin of defeat or victory for the losing and winning parties.

In a 2019 paper in Physical Review E, SFI collaborator Stefan Bornholdt (Institute Rudjer Boskovic) and his colleagues present a voter model that explains what drives public opinion toward stalemate. In a word, it is repulsion. As voters are either convinced or repelled by statements, they can change sides or switch to an undecided state if they come to doubt their former opinion. In a contentious debate, when a voter is repelled by at least one out of four statements, a phase transition occurs where neither party can win in the long run and no clear winner emerges. To shift these dynamics from stalemate to majority, the study offers several recommendations for moving away from hostile statements and toward rational discourse. Their most radical proposal? “To declare results as invalid where the difference between yes and no is less than ten percent.”

Read the paper at doi.org/10.1103/PhysRevE.100.042307