GettyImages-483209582[1]

Republican presidential candidates arrive on stage for the Republican presidential debate on August 6, 2015 at the Quicken Loans Arena in Cleveland, Ohio. From left are: New Jersey Gov. Chris Christie; Florida Sen. Marco Rubio; retired neurosurgeon Ben Carson; Wisconsin Gov. Scott Walker; real estate magnate Donald Trump; former Florida Gov. Jeb Bush; former Arkansas Gov. Mike Huckabee; Texas Sen. Ted Cruz; Kentucky Sen. Rand Paul; and Ohio Gov. John Kasich. (MANDEL NGAN/AFP/Getty Images)

How did Donald Trump become the presumptive 2016 Republican nominee for president of the United States?

It’s a common question these days, and scientists at the Network Science and Technology Center (NeST) at Rensselaer say the answer can be found in social opinion dynamics and the influence of a committed minority.

The scientists—Boleslaw Szymanski, NeST director and the Claire and Roland Schmitt Distinguished Professor of Computer Science; Chjan Lim, professor of mathematical sciences; and William Pickering, doctoral student in mathematical sciences—used mathematical models to investigate how opinions spread when there is unusual dissent or diversity. That was the case for much of the 2016 Republican primary season, which began with 17 candidates seeking the party’s nomination.

The scientists found that, under such circumstances, members of a small, committed minority can quickly spread their opinion to those who are uncommitted. In addition, the success of the committed minority increases with the diversity of opinion among the uncommitted group. The more fragmented the group, the easier it is for the group to be influenced by a smaller number of committed members.

In other words: If divided, easily conquered.

“In a situation where there are many small groups and no dominant opposition, stability is broken. Sooner or later, one of the small minorities will win,” Szymanski said. “Too much dissent between individuals makes them susceptible to even a few zealots.”

In the scientific community, committed members are often referred to as “zealots” for the sake of brevity.

“This division of the majority opinions allows for even initially small committed groups to thrive,” Lim said. He stressed, however, that the research could not predict which committed minority opinion would become dominant.

The scientists found that, under such circumstances, members of a small, committed minority can quickly spread their opinion to those who are uncommitted. In addition, the success of the committed minority increases with the diversity of opinion among the uncommitted group. The more fragmented the group, the easier it is for the group to be influenced by a smaller number of committed members.

The research findings are discussed in “Analysis of the high-dimensional naming game with committed minorities,” in the May issue of Physical Review E. Pickering is the lead author.

The Rensselaer team used a new variation on the Ehrenfest urn model to assess the impact of zealots on a larger group. Developed in 1907 to explain the diffusion of gas molecules between two urns, the Ehrenfest model has since served as the basis for other generalizations in physics. The Rensselaer team has extended the application of the Ehrenfest model by inventing a new class of similar urn models to study problems in sociology and biology.

“The key to our innovation is that the agents in the model influence each other through pair-wise interaction—one person influencing another,” Pickering said. “That’s quite distinct from gas particles bouncing around in a closed container, as in the Ehrenfest model.”

With support from his thesis adviser Lim, who suggested extending generating function methods to the urn models, Pickering developed mathematical theories and solutions for the new model. The Rensselaer team then put the theories to the test as part of their research on the influence of committed minorities.

“We arrived at fairly detailed solutions for the behavior of the model in terms of opinion diversity and zealotry,” Pickering said. His work on the theories and solutions earned him the Mathematical Sciences Department’s Richard and Maureen DiPrima Graduate Research Award in Mathematics and The Joaquin B. Diaz Prize, both for 2016.

The recent findings complement Szymanski’s earlier research on the tipping point required for the spread of ideas. That research, published in 2011 by Szymanski, Lim, and other scientists at Rensselaer, found that if just 10 percent of the population holds an unshakeable belief, the belief will always be adopted by the majority of society.

The number of people you need to sway opinion gets smaller and smaller as the number of opinions gets larger and larger, and there is a mathematical reason why this happens—Bolek Szymanski

The 10 percent tipping point applies when there are two competing opinions. The new research indicates that the tipping point will fall below 10 percent when society holds a wide variety of opinions on the given subject. In fact, the greater the diversity of opinion, the lower the tipping point.

“The number of people you need to sway opinion gets smaller and smaller as the number of opinions gets larger and larger, and there is a mathematical reason why this happens,” Szymanski said.

The 2003 California gubernatorial recall election is an excellent example. The recall ballot featured 135 candidates. The diversity and division cleared the way for the election of Arnold Schwarzenegger to his first political office.

The Rensselaer study is part of an extensive portfolio of research at NeST, which brings together scientists from a variety of disciplines—including sociology, physics, computer science, and engineering—to explore social cognitive networks and the behaviors that govern their dynamics and evolution.

This multidisciplinary approach is typical of The New Polytechnic, which recognizes that today’s global challenges and opportunities cannot be addressed by the most talented person working alone. The New Polytechnic enables collaboration using the latest, most advanced tools, technologies, and approaches to address the complex problems of the world.

The Rensselaer research on committed minorities was supported, in part, by the U.S. Army Research Office, the Army Research Laboratory, and the Office of Naval Research. The Army is the principal funder of NeST.