Why are close elections so common?

Why are close elections so common?

By Manon Bischoff

The whole world is eagerly awaiting the American presidential elections on November 5, 2024. According to a poll averageIn mid-October, about 49 percent of respondents said they would vote for Democrat Kamala Harris and about 47 percent said they would vote for Republican Donald Trump. The elections appear to be a neck-and-neck race.

Surprisingly, the US is not an isolated case. When the people of a democratic country have to decide between two alternatives, the elections are usually very close – as was the case with Brexit and with the Polish presidential elections in 2020. The decisive question is then: what explains these observations?

The answer certainly has a large psychological, demographic and sociological component. Yet the behavior of large groups of people can easily be described with mathematical models. And this is exactly what physicists Olivier Devauchelle of Paris City University, Piotr Nowakowski, now at the Ruđer Bošković Institute in Croatia, and Piotr Szymczak of the University of Warsaw have done.

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In an article published in the magazine Physical assessment E April 2024they examined the election results of democratic states since 1990 and created a model that describes them. In this way, they were able to identify a mechanism that explains close election results.

In May 2016, a referendum shook the European continent. Contrary to expectations, the British electorate voted with a narrow majority of 51.9 percent in favor of leaving the European Union in the so-called Brexit decision. The result is all the more astonishing when you look at the data from before the actual vote. In the opinion polls the votes were very unevenly distributed. For example, in October 2014, the ‘remainers’ (those who wanted to remain part of the EU) were almost 20 percentage points ahead of the ‘Brexiters’..” The closer voting day got, the more the polls pointed to a 50-50 result.

A similar picture emerges when we look at the Polish presidential elections on July 12, 2020. President Andrzej Duda, who was seeking re-election and had no party membership but was supported by the nationalist Law and Justice party, rebelled against the economically liberal politician at the time Rafał Trzaskowski. In the polls in May 2020Duda still led with about 54 percent of the vote, but on election day he received only 1 percent more votes than his rival. Here too it became clear that the closer election day approached, the smaller the differences in election results became.

To model an emergent equilibrium in two-party sentiment, you might initially assume, as is common in game theory, that each voter tosses a coin. The result would then be almost 50-50, the chance of heads or tails. However, such a simplified model does 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 east of the country were more likely to vote for Duda, while citizens in the west were more likely to vote for Trzaskowski.

So it seems that voters influence each other. To describe this mathematically, Devauchelle, Nowakowski and Szymczak used the Ising model, which is well known in physics. The 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. The units influence each other by trying to align themselves in the same way. The strength of the interaction between adjacent units determines the condition of the material. If the interaction is weak, the result is a material that is chaotic (without magnetization), but as the interaction strength increases, a phase transition occurs in which magnetization occurs. In this case, the majority of all units have the same orientation.

Applied to elections, this description would amount to an unequivocal outcome. Such situations do indeed occur in history, but “usually in countries that do not have a large population. The researchers noticed this when they analyzed the election results of the past hundred years. “Countries with fewer than about a million voters tend to reach a consensus,” Devauchelle told Phys.org“while the (voters) of larger countries generally converge towards (an evenly distributed state of voter sentiment), even if one camp was clearly ahead in the polls at the start of the elections.”

To ensure that the Ising model can also model opinion polls and election results in densely populated countries, the physicists introduced a ‘non-conformity factor’ that introduces a negative attitude towards the camp leading in the polls. Together with Nowakowski and Szymczak, he simulated such voter behavior. To do this, the three physicists used a network in which interconnected units influence each other.

The non-conformity factor produced a surprisingly realistic result. An initially balanced state evolves over time into a 50-50 electoral outcome. Furthermore, the network splits into two parts, with adjacent units usually occupying the same state. However, the researchers emphasized in the article that social networks are much more complex. Their structure is not limited to two dimensions, and the connections between people can be much more complicated. Nevertheless, to a first approximation the model produces results close to real-world scenarios.

However, the model is not so easy to apply to the American presidential elections. This is because citizens do not vote directly for a presidential candidate, but through votes in the electoral college. This means that a majority of the population does not necessarily determine the outcome of the elections. So it is unclear whether Harris or Trump will win the race. But one thing can be said: the elections are undoubtedly very close.

This article originally appeared in Spectrum of Science and is reproduced with permission.