Modeling suggests friendships may lead to lopsided elections

Have you ever thought about not voting because your favorite candidate seems guaranteed to win? New Cornell research uses mathematical modeling to show that type of thinking can have the opposite effect, leading to the election of politicians who do not represent the preferences of voters as a whole.

Even more surprising, the culprit in this disproportionate outcome is not political wrongdoing: it may be your network of friends, whose predictions about a likely winner can distort your sense of the election outcome and the value of your vote.

The group’s paper, “How a Minority Can Win: Unrepresentative Results in a Simple Voter Turnout Model,” was published November 22 in Physical Review E. The lead author is doctoral student Ekaterina Landgren.

The research was led by Stephen Strogatz, Jacob GoldShurman Professor of Applied Mathematics in the College of Arts and Sciences and lead author of the paper.

“In democracies, it is very important to consider that sometimes the candidate who gets the most votes in an election or a referendum is not the one that most people really like,” Landgren said. There are some structural reasons for this. There is manipulation, and there are evil agents. But our model focuses on a situation where this is not created on purpose, but rather stems from the way people assess whether or not their vote will make a difference based on the people they know and the things they see around them.”

Rather than sifting through electoral data and polling results, the researchers relied on a simple mathematical model to randomly generate a variety of friendship networks, each with different assumptions and different levels of interaction, along with other factors, such as geographic proximity. After introducing these parameters in code, they tested the scenarios in simulations and then analyzed the statistics of the results, oftentimes mathematically validating the results.

said Jonas Joll, a postdoctoral researcher at the Cornell Center for Applied Mathematics and one of the authors of the paper. But it is important that this is a model. We don’t believe this is an accurate representation of reality, but it is an investigation into how the form and structure of social networks affect elections.”

Modeling highlighted two conditions under which social ties can veer: “laxity,” where people don’t bother voting because they are sure, based on their friends’ expectations, that their preferred candidate will win; and “gloom,” where people abstain from voting because they think their candidate is going to lose anyway.

At the same time, some people in the minority are motivated to vote openly because their preferred candidate appears weak, and this can, paradoxically, lead to victories for politicians who do not have the support of the majority.

“In networks where there is some tendency to search for like-minded people, it is easier for the minority to convince themselves that they are in danger, and that elections will be very close, compared to the majority,” Landgren said. “What’s interesting about it, from a math perspective, is that the majority has more accurate information, on average, about the state of the friendship network, or the general opinions that exist in that network. So the majority sees that there are more majority nodes, and that’s true. The minority sees That there are roughly equal numbers of majority and minority nodes, which is not true, but that is exactly the effect that allows them to win.”

Of course, voters can be influenced by many different sources, from news coverage to social media echo chambers. However, the researchers’ mathematical modeling provides an effective way to isolate the effect of social ties on voters’ often opaque decision-making processes and could also point the way to future studies that explore many other factors in driving people to elections.

“Although our model is very simplistic, we were surprised by a lot of its behavior,” Strogatz said. So just imagine how difficult it is to predict voter turnout in reality. This is yet another reminder that the social sciences may be the hardest science of all.”

The research was supported by a postdoctoral fellowship at the Cornell Center for Applied Mathematics, the National Science Foundation and the National Institutes of Health.

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