# Modeling belief systems

October 24, 2016It's no secret humans are social creatures with beliefs that are, literally, all over the map. What wasn't known was how those beliefs are influenced by our social interactions. Now, in a breakthrough study led by a UC Santa Barbara sociologist, scholars have developed a mathematical model that describes the relationship between belief systems and interpersonal influence, and what happens when underlying beliefs change.

According to the paper's lead author, Noah E. Friedkin, a professor of sociology at UCSB, a belief system in a group -- religious or political, for example -- depends on a set of interlocking beliefs. Known as an opinion dynamics model, it's a collection of attitudes, opinions, certainties or "cognitive orientation" towards a person or statement. "A person's belief on one subject may be dependent on their beliefs in other issues," he explained. "There's an underlying cognitive consistency that links multiple beliefs."

In the paper, "Network Science on Belief System Dynamics Under Logic Constraints," which appears in the current issue of

*Science*, Friedkin and his co-authors extend that opinion dynamics model to cover belief systems composed of interdependent beliefs. As an example, he noted, religion typically consists of an interlocked set of beliefs. If a person believes in a supreme being, he or she will also believe in the Earth's origin story, the supreme being's rules of worship and so on. Those beliefs are buttressed by people who share them. "If you know how someone feels about one issue, you can pretty much logically infer, on the basis of belief system structure, that they hold certain positions on other issues."

The mathematical model described in the paper, Friedkin said, addresses two processes. One is the "interpersonal influence system" that helps shape a person's beliefs. The other is what happens when a belief changes, and how it recalibrates a person's beliefs on other, linked issues. "For example," he said, "if you felt strongly about one thing and I can convince you to change your opinion on it, you would go home and, in an internal process, your brain would reorganize your beliefs that depend on the belief that has been changed."

The paper uses the Iraq War as an example of how beliefs, or "logic structures," function. It notes three statements that underlay the belief that the U.S. preemptive invasion of Iraq was acceptable. One, Saddam Hussein has a stockpile of weapons of mass destruction; two, Hussein's weapons of mass destruction are real and present dangers to the region; and three, a preemptive invasion of Iraq would be a just war.

A "high certainty of belief" in the first statement implied a concomitant certainty in statements two and three, the paper noted, and polling indicated a strong majority of Americans supported the war. However, the failure to find any weapons of mass destruction negated statement one and effectively led to a cascading rejection of statements two and three. "If you don't accept that first premise, then it's difficult to justify or accept the statement that a preemptive war is justified," Friedkin noted. "The cascade of changes occur on multiple issues, and that cascade has a structure to it, which is the logic structure that links a set of issues or beliefs."

Looking ahead, Friedkin said this new mathematical model of opinion dynamics could give sociologists the tools to study overlooked complex issues. "My hope, and the hopes of my collaborators," he said, "is that this will trigger more work on this, because the literature and the opinion dynamics have been focused on single-issue dynamics. We hope this article will trigger research on a more complex form of dynamics in which positions on multiple interdependent issues are being modified by influence network processes, and apply it to a variety of different observable cases."

The paper was the result of interdisciplinary and international collaboration. The other authors are Anton Proskurnikov, a mechanical engineer at the University of Groningen in The Netherlands; Roberto Tempo, a social control theorist at the National Research Council in Torino, Italy; and Sergei Parsegov, a mechanical engineer at the Russian Academy of Sciences.

"It's an interesting field," Friedkin observed, "because without a mathematical model you simply cannot predict the destinations of the individuals' opinions, where they end up, because these influences play out in a network structure. With both direct and complex indirect interpersonal influences at play, a mathematical model of the dynamical system is required to provide an explanation."

-end-

University of California - Santa Barbara

**Related Mathematical Model Articles:**

How big brains evolved could be revealed by new mathematical model

A new mathematical model could help clarify what drove the evolution of large brains in humans and other animals, according to a study published in PLOS Computational Biology.

A new mathematical model could help clarify what drove the evolution of large brains in humans and other animals, according to a study published in PLOS Computational Biology.

'Field patterns' as a new mathematical object

University of Utah mathematicians propose a theoretical framework to understand how waves and other disturbances move through materials in conditions that vary in both space and time.

University of Utah mathematicians propose a theoretical framework to understand how waves and other disturbances move through materials in conditions that vary in both space and time.

Mathematical model reveals parental involvement can 'immunize' students from dropping out

The bad news? It only works up to a point.

The bad news? It only works up to a point.

Mathematical model limits malaria outbreaks

Mathematical models can effectively predict and track malaria transmission trends, ultimately quantifying the efficiency of various treatment and eradication strategies in high-risk regions.

Mathematical models can effectively predict and track malaria transmission trends, ultimately quantifying the efficiency of various treatment and eradication strategies in high-risk regions.

Scientists create first viable mathematical model of a key anti-Salmonella defense system

Scientists have created the first validated mathematical model of an important cellular defense mechanism against the bacterium Salmonella, according to a new study in PLOS Computational Biology.

Scientists have created the first validated mathematical model of an important cellular defense mechanism against the bacterium Salmonella, according to a new study in PLOS Computational Biology.

Mathematical algorithms calculate social behavior

For a long time, mathematical modelling of social systems and dynamics was considered in the realm of science fiction.

For a long time, mathematical modelling of social systems and dynamics was considered in the realm of science fiction.

Researchers create first 3-D mathematical model of uterine contractions

By studying the electric activity that causes uterine contractions in pregnant women, researchers at Washington University in St.

By studying the electric activity that causes uterine contractions in pregnant women, researchers at Washington University in St.

Exploring the mathematical universe

A team of more than 80 mathematicians from 12 countries has begun charting the terrain of rich, new mathematical worlds, and sharing their discoveries on the Web.

A team of more than 80 mathematicians from 12 countries has begun charting the terrain of rich, new mathematical worlds, and sharing their discoveries on the Web.

New mathematical model challenges aggressive antibiotic treatments

Antibiotic resistance is one of the most challenging problems in modern medicine.

Antibiotic resistance is one of the most challenging problems in modern medicine.

A mathematical advance in describing waves

Two UB mathematicians have published a new paper that advances the art -- or shall we say, the math -- of describing a wave.

Two UB mathematicians have published a new paper that advances the art -- or shall we say, the math -- of describing a wave.

**Related Mathematical Model Reading:**

## Best Science Podcasts 2019

We have hand picked the**best science podcasts**for 2019. Sit back and enjoy new science podcasts updated daily from your favorite science news services and scientists.

**Now Playing: TED Radio Hour**

**Changing The World**

What does it take to change the world for the better? This hour, TED speakers explore ideas on activismâwhat motivates it, why it matters, and how each of us can make a difference. Guests include civil rights activist Ruby Sales, labor leader and civil rights activist Dolores Huerta, author Jeremy Heimans, "craftivist" Sarah Corbett, and designer and futurist Angela Oguntala.

**Now Playing: Science for the People**

**#520 A Closer Look at Objectivism**

This week we broach the topic of Objectivism. We'll be speaking with Keith Lockitch, senior fellow at the Ayn Rand Institute, about the philosophy of Objectivism as it's taught through Ayn Rand's writings. Then we'll speak with Denise Cummins, cognitive scientist, author and fellow at the Association for Psychological Science, about the impact of Objectivist ideology on society. Related links: This is what happens when you take Ayn Rand seriously Another Critic Who Doesn’t Care What Rand Thought or Why She Thought It, Only That She’s Wrong Quote is from "A Companion to Ayn Rand"