Why do close elections happen so often?

Why do close elections happen so often?

Manon Bischoff

The whole world is looking forward to the US presidential election on November 5, 2024. As of mid-October, about 49 percent of respondents said they would vote for Democrat Kamala Harris, and about 47 percent said they would vote Republican, according to one poll average. Donald Trump. The election is likely to be close.

Surprisingly, this is not unique to the United States. When people in democracies decide between two choices, elections are usually very close, as was the case with Brexit and the 2020 Polish presidential election. Therefore, the most important question is: what is the cause of these observations?

The answer certainly has a lot to do with psychological, demographic, and sociological factors. Nevertheless, the behavior of large groups of people can be very well explained using mathematical models. And this is exactly what Olivier Devauchel, a physicist at the University of the City of Paris, and Pyotr Nowakovsky, currently at Boskovy University in Russia, have done. It was carried out by Piotr Simczak from the Croatian Institute and the University of Warsaw.

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In a paper published in a magazine Physical Review E In April 2024, they studied election results in democracies since 1990 and created a model to explain them. In this way, they were able to identify mechanisms that explain close election outcomes.

In May 2016, a referendum shook continental Europe. Contrary to expectations, British voters supported leaving the European Union by a narrow margin of 51.9 percent in the so-called Brexit decision. The results become even more surprising when you consider actual pre-vote polling data. The polls showed that the vote was very lopsided. For example, in October 2014, “Remainers” (those who want to remain in the EU) outnumbered “Leave” supporters by about 20 points. As voting day approached, opinion polls showed a 50-50 split.

A similar picture emerges when we look at the Polish presidential election on July 12, 2020. President Andrzej Duda, who was seeking re-election at the time, was an independent but supported by the nationalist Law and Justice Party and ran against his economic policies. Liberal politician Rafa&lStroke Trzaskowski. In a May 2020 opinion poll, Duda still led with about 54% of the vote, but on election day he had won just 1% more votes than his rival. Here too, it became clear that the gap in opinion poll results narrowed as voting day approached.

To model the new equilibrium in two-party sentiment, we can first assume that each voter flips a coin, as is usual in game theory. In that case, the result could be closer to 50/50, giving you either heads or tails. However, such simplistic models do not reflect reality. For example, if you look at the results of the Polish presidential election, it quickly becomes clear that the votes were not randomly distributed. Citizens in the eastern part of the country were more likely to vote for Duda, while those in the western part were more likely to vote for Trzaskowski.

In other words, voters seem to influence each other. To explain this mathematically, Devauchelle, Nowakowski, and Szymczak used the Ising model, which is well known in physics. This model simulates, among other things, the behavior of magnetic materials. In the Ising model, these consist of small magnetic units arranged in a regular grid. Units influence each other by trying to coordinate in the same way. The strength of the interactions between adjacent units determines the state of the material. When the interaction is weak, the material becomes chaotic (no magnetization), but when the interaction is strong, a phase transition occurs that results in magnetization. In this case, the majority of all units will have the same orientation.

Applying this explanation to elections would equate to obvious results. Situations like this have indeed occurred throughout history, but “almost always occur in countries without large populations,” researchers found when analyzing election results over the past 100 years. “Countries with fewer than about 1 million voters tend to reach an agreement,” DeVauchel told Phys.org. At the start of the election, he was leading in opinion polls. ”

To enable the Ising model to also model polls and election results in populous countries, physicists introduced a “misfit” element that resulted in negative attitudes toward the camp leading in the polls. . Together with Mr. Nowakowski and Mr. Simchak, he simulated the behavior of such voters. To do this, the three physicists used a network of interconnected units that influenced each other.

The mismatch factor produced surprisingly realistic results. States that are initially balanced develop over time until the election results are 50-50. Furthermore, the network is divided into two parts, and adjacent units usually occupy the same state. However, the researchers stressed in their paper that social networks are much more complex. Its structure is not limited to two dimensions, and connections between people can be even more complex. Nevertheless, as a first approximation, the model yields results close to real-world scenarios.

However, applying this model to the US presidential election is not so easy. This is because citizens do not vote directly for presidential candidates, but through electoral votes. This means that the majority of the population does not necessarily decide the outcome of the election. Therefore, it is unclear whether Harris or Trump will win the election. But one thing is clear: the election is definitely very close.

This article was first published Wissenschaft spectrum Reprinted with permission.