Applied mathematics students at Tufts may have the opportunity to cross over into social science. Two professors are pushing the boundaries of interdisciplinary math by investigating problems in social sciences through their research.
Professor Bruce Boghosian has been working on modeling wealth inequality for about five years, beginning during his time as president of the American University of Armenia. The country, which became independent after the breakup of the Soviet Union in 1991, underwent drastic liberalization and, like many other former Soviet states, quickly became an oligarchy, according to Boghosian.
“Unfortunately, it’s easier to create an oligarchy than it is to break loose from it,” Boghosian said. “It is an unfortunately stable form of government.”
Boghosian’s work now sets out to model the inequality that results from free markets over time. His model illustrates the increasing trend of asymmetry in the economy as wealth becomes concentrated in fewer and fewer hands.
“The accuracy with which we’re able to match the wealth distributions is remarkable,” he said. “To my knowledge, no other first-principles theory is able to achieve the same accuracy. That’s what grounds it in reality, somehow, and makes it more than just a mathematical model.”
He explained that the belief that the current economic system will result in equilibrium dates back to the Enlightenment, during which freedom of transaction was embraced following a period of restricted economy in Europe.
“You can understand why people regarded the opportunity to engage in transactions of one’s own free will as a sort of freedom from that, but there’s a bias that’s hidden in it. There’s an asymmetry, and it’s not the least bit obvious,” Boghosian said. “I wish that it didn’t require so much mathematics to describe.”
Boghosian noted that his work takes a different approach than traditional economic models of equilibrium. However, economics professors at Tufts have been generally receptive to his work.
“They’ve all been really encouraging, in fact, and supportive of it,” he said. “I’m not sure they believe it, but they’re welcoming to an outsider who is really just learning about economic issues.”
Boghosian has also taught two courses in the Department of Mathematics regarding wealth inequality, which he said generated significant levels of student interest.
Senior Chengli Li, an applied mathematics major, has worked with Boghosian on his research, including as part of the summer scholars program this year.
“I think it’s really interesting to solve economic problems from a math perspective,” Li, who is also an economics major, said. “I think from the math perspective it’s a really interesting new way of looking at it.”
Li said that she enjoyed the opportunity to apply her knowledge of mathematics across disciplines and toward issues which she has observed in the world.
“I’m an international student, I’m from China, so the place where I came [from] was a mixture of really poor people and really wealthy people,” she said. “So I know there’s an issue, and this research is really able to apply what I’ve learned to the things that I’ve heard at school or the things that I’ve seen.”
Ultimately, Boghosian said, there must be some outside intervention to counter the continued concentration of wealth.
“One thing that we found clearly is that redistribution is the only thing that keeps an economy stable,” Boghosian said. “I mean, there can be many mechanisms for redistribution, but a redistributive term in the wealth distribution evolution equation is important.”
Boghosian said this redistribution could be done through a variety of mechanisms. He added that transparency was of critical importance because many people hide their wealth.
“There’s an advantage to taxing wealth directly, even if it’s a tiny tax, not enough to hurt anybody, but it would oblige people to declare their wealth in the same way they declare their income,” he said.
He hopes that by presenting his data, the political will of people may be more easily impacted to make changes.
“In my opinion, one of the things that can influence political will is the clear demonstration that the system we have now, even though it may seem fair, isn’t,” he said. “It is inherent and endogenously unfair and biased.”
While Boghosian’s work has vast implications on pragmatic economic policy, he said he is focused primarily on using his model to analyze current data from around the world.
“It would be wonderful in the future to be able to connect our models with real public policy, but that will take years,” he said. “That’s something that we are working on, and people are beginning to think about, but it’s not ready for implementation yet.”
Elsewhere in the mathematics department, Associate Professor Moon Duchin is also addressing social issues through her ongoing research in gerrymandering. Her work uses geometry to look into the potential unfair drawing of U.S. districts in order to benefit particular political groups, also known as gerrymandering. Duchin said that she is on sabbatical this semester while pursuing her gerrymandering research full-time.
“Because [voting] is done by districts, it depends really heavily on what those districts look like, and so the question is, ‘What should be the rules about the shapes of districts?’” she said. “If you have some rules about what the [districts] can look like, that limits the power of the map-drawer.”
She said that, while members of the mathematics department do not often do research into social issues, applied math does have a strong presence in some more traditionally related fields.
“One thing that’s cool about the mathematics department at Tufts is that it has both pure and applied mathematicians in the same department,” she said.
However, Duchin herself does not have a background in applied mathematics. She said that she became interested in the topic of gerrymandering while preparing to teach the math of social choice class at Tufts, after noticing that work on the geometry of districts was out of date.
“For me, this is a turning point, because my background is in theoretical, pure mathematics,” Duchin said. “This is the first time I’ve gotten into something so applied. And I didn’t fully realize in the past that cutting-edge math could be applied to politics instead of the traditional crossover fields like physics, chemistry and biology.”
Duchin said that the type of mathematical work associated with social sciences like economics and political science is often called quantitative social science. Although Tufts does not have a program in that field, Duchin pointed out the Science, Technology, and Society (STS) major, of which she is the director, as an example of bridging the gap between social science and humanities.
“For students who are interested in crossing over between STEM fields and books and real life, that’s exactly what niche STS is trying to fill — to be a bridge between math and engineering and other technical areas and the practical application in human culture,” she said.
Duchin said that Tufts’ encouragement of interdisciplinary and civically engaged work has been a positive influence on her own endeavors. For example, she has worked with professors in the political science department as well as members of the Jonathan M. Tisch College of Civic Life.
“As you see, Tufts is an amazing place to be,” Duchin said. “It’s exciting to be here because there are really not that many places that are as serious about interdisciplinarity as Tufts, and the Tisch College focus on integrated civics is unique. So for me, it’s been a real treat to be here and work with people in so many other fields.”