If you have ever tried to change someone’s mind on an important issue — how to vote, for example — you know swaying an entrenched opinion is no easy task. Studying just how, when, and why opinions change and the many variables that affect that complex process might be just as difficult.

That difficulty didn’t deter researchers in Virginia Tech’s Department of Biomedical Engineering and Mechanics, who recently used advanced mathematics and computational modeling to analyze opinion trends surrounding notable public policy. Through their research, they were able not only to rank the importance of several key factors affecting legislation on same-sex marriage in the United States, but also to predict when states would vote to legalize it.

Published in Royal Society Open Science, the study used real-world datasets to examine the interactional dynamics affecting the opinion formation of senators and state electorates over 19 years, leading up to the national legalization of same-sex marriage in 2015. During their analysis, the researchers first identified a variety of factors that affected opinions on same-sex marriage. Within that pool of factors, they were then able to rank geographical distance as the most important influence on state electorates and ideological distance as the most important influence on individual senators.

States that were geographically close to one another tended to vote the same way around the same time, but states far away from each other did the opposite. The same held true for senators who were close to each other in ideology.

In the Complex Systems Laboratory at Virginia Tech, Subhradeep Roy (left) and Nicole Abaid discuss a mathematical formula used in computational modeling. Roy and Abaid analyzed extensive datasets to identify and rank important factors influencing opinions and public policy on same-sex marriage legislation in the United States. They also used their findings to build a predictive model of the law’s adoption.
In the Complex Systems Laboratory at Virginia Tech, Subhradeep Roy (left) and Nicole Abaid discuss a mathematical formula used in computational modeling. Roy and Abaid analyzed extensive datasets to identify and rank important factors influencing opinions and public policy on same-sex marriage legislation in the United States. They also used their findings to build a predictive model of the law’s adoption.

“Basically, if states are within a certain geographical distance or ideological distance, they kind of do the same thing,” said Nicole Abaid, an assistant professor in the Department of Biomedical Engineering and Mechanics in the College of Engineering and the study’s co-author. “States respond more to geography, but senators respond more to ideology.”

The data also revealed that states’ adoption of same-sex marriage legislation was most dependent on senators’ opinions one year beforehand. Essentially, when senators changed their minds on same-sex marriage, state legalization was most likely to follow about one year later.

Abaid began the research project several years ago with Subhradeep Roy, a then-doctoral student in Virginia Tech’s engineering mechanics program and the study’s lead author. The study was part of a larger effort to understand the factors that play important roles in opinion formation at the individual and group level.

Public policies, like same-sex marriage legislation, tend to aggregate interactions across a wide cross section of social frameworks. They are ideal examples of the intricate negotiations that make up opinions — with the added benefit of measurable data.

“We’re trying to understand what’s happening and why it’s happening,” said Abaid. “How do opinions change, and what variables can we measure that affect those changes? Some things we can measure, but some things we can’t. We want to understand the larger model based on what we can track.”

Abaid and Roy first used data on state law adoption and senatorial support from 1996 to 2014 to identify opinion trends. Then they used that information to build a state law adoption model that demonstrated predictive power with those same real-world datasets.

“The real-world datasets helped us uncover the driving factors behind these opinion trends, and we incorporated these factors into a model that can be used for prediction,” said Roy. “This type of model can be adapted to predict opinion trends on other public policies.”

Roy was interested in the study’s demonstration of how researchers can use applied mathematical techniques to analyze real-world datasets in order to identify factors that influence opinions.

Now a postdoctoral associate in Virginia Tech’s Department of Philosophy in the College of Liberal Arts and Human Sciences, Roy has teamed up with Benjamin Jantzen, an assistant professor of philosophy and a computer scientist, to develop a machine learning algorithm that detects predominant system variables from time series data. This interdisciplinary research, like his work on collective opinion formation, was inspired by his studies of complex systems.

Benjamin Jantzen, an assistant professor of philosophy, conducts research on ”robot scientists.”
Benjamin Jantzen, an assistant professor of philosophy, conducts research on ”robot scientists.”

Benjamin Jantzen, an assistant professor of philosophy, conducts research on ”robot scientists.”

Ultimately, Roy hopes these types of mathematical tools will help people better understand the real-world phenomena that are happening around them.

Both Abaid and Roy said researchers will probably never be able to track and measure the untold number of personal factors that affect complex processes like collective opinions and public policy. However, their study on same-sex marriage legislation is a good example of how data can evidence certain types of interactions and influences after the fact.

“A lot of times, we like to think our opinions are pristine, but they’re not. There’s a reason advertising budgets are so huge,” said Abaid, adding that some aspects of opinion formation are probably subconscious.

“You think you’re not subject to certain types of influences,” she said, “but you are.”

Written by Emily Roediger