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Do the math? Only if I agree with it!

Better arithmetic is no match for partisan politics

It’s comforting, in these polarized times, to blame the idiots. Our failure to come together on issues like health care and gun control, climate change and economic policy, isn’t our fault, we like to tell ourselves. It’s a result of the talk-radio blowhards, the cable TV know-nothings, and the blind partisans—on the left and right—too dumb to look at the data and do the math.

But now new research is suggesting something different. The problem is not people who can’t do the math. The problem is the ones who can.

In a new working paper, Yale Law School’s Dan Kahan and three other researchers make the case that those more skilled at math are less likely to come to the correct conclusion on controversial matters—even when the numbers to support that conclusion are clear, empirical, and staring them in the face.

In the study, conducted this past spring, over 1,100 participants were asked to use numbers to assess whether a particular intervention had worked—either a skin rash treatment or a gun ban. In assessing the rash treatment, which had no political implications, those with lower “numeracy,” or math skills, were, as you might guess, far less successful than their “high-numerate” peers: They were likely to get the question right about one-third of the time, compared to two-thirds of the time for the group with better math skills.

But the question about the gun ban revealed something that Kahan called “shocking and really disturbing.” When doing the math yielded an answer that contradicted a participant’s politics, the high-numerates were about as likely to get it wrong as their low-numerate counterparts.


High-numerate conservative Republicans were far more likely to come to the right, data-based conclusion in the gun ban question if they had been told that crime increased—a result that squares with their ideology. High-numerate liberal Democrats were far more likely to get it right if crime decreased. Perhaps most troubling, Kahan found, the numerate people were more polarized than those who struggled with the math: They were 45 percentage points more likely to get the right answer if the data backed up their views than if it didn’t. Low-numerate people, by comparison, were far less polarized.


“This study suggests that they’re using their greater numeracy in a kind of strategic, opportunistic way,” said Kahan, a professor of law and psychology. “They’re using their better ability to make sense of the evidence in a way that gratifies their state and fits their ideology.”

The research, which was funded by the National Science Foundation, adds to the growing evidence that politics tends to put our rational brains on hold: We’re highly motivated to assess facts in ways that square with our ideologies, even when the facts specifically contradict our views. What’s significant about these new findings, said Peter Ditto, a professor of psychology and social behavior at the University of California Irvine, is that even empirical data—and math skill—isn’t enough to overcome the power of cultural persuasion. Scientifically speaking, “that’s a real advance,” Ditto said. “The people who are the smartest at this are most wrong about it—at least when it challenges their beliefs.”

Whether there’s a way out of this conundrum—and a possible way to help heal our dysfunctional, ultra-polarized civic discourse—isn’t yet clear. It’s not easy—or, for politicians and interest groups, desirable—to depoliticize hotbutton issues, and researchers disagree about whether even more math education could help. But one thing is apparent: We might as well stop insisting we’re the only ones who understand the data, because our math is probably subject to our beliefs, too.

N umeracy is about

more than just numbers. It’s about our ability to process information and reason through situations involving math—something we do all the time. “Numbers are everywhere in everything that we do,” said Ellen Peters, a professor of psychology at Ohio State University and a coauthor of this new research. “And generally,” she added, “it’s better to be highly numerate.”


Studies have found that patients with strong math skills are more likely to understand medical risks and less likely to rely on anecdotal information when making medical decisions. Low numeracy, by contrast, is associated with a litany of health issues, including poor disease management skills and increased body weight. Not surprisingly, numerical skills also affect our personal wealth. According to recent research, households with two highly numerate spouses are eight times wealthier than households with two spouses exhibiting low numeracy.

Yet for all the advantages that high numeracy might offer, it comes with quirks that, Peters said, “can trip us up.” In a survey published last year in the journal Nature Climate Change, Kahan, Peters, and their coauthors found that people with the highest degrees of science literacy and technical reasoning weren’t the most concerned about climate change. On the contrary, these highly numerate folks were most polarized on the issue.

Surprised and intrigued, the researchers set out to test this finding with the current experiment, providing the 1,100 participants with numbers to help them calculate the efficacy of two different matters: a skin rash treatment and a gun ban. They were then asked to determine, based on the numbers, whether the treatment helped the skin rash get better or worse and whether the gun ban led to an increase or decrease in crime.


Some participants received data indicating the measure had succeeded (the treatment worked, the ban led to a decrease in crime), while others got data indicating the opposite (the treatment failed, the ban led to an increase in crime). But no matter which numbers the participants received, the task was the same. All they needed to do was calculate a relatively simple proportion, and the correct answer would be obvious.

With the skin rash question, the results were straightforward. Low-numerate people struggled to come to the correct, data-supported conclusion no matter their political leanings. They were likely to get it right no better than about 38 percent of the time, compared with a success rate of about 65 percent among high-numerate people.

The gun ban calculation, however, brought out the subjects’ political biases in problematic ways. When the gun-ban experiment suggested that crime went down, high-numerate liberals, pleased with the results, were likely to get the answer right about 70 percent of the time, while high-numerate conservatives, faced with an upsetting answer, were likely to get it right about 20 percent of the time. But when the experiment suggested crime went up after the gun ban, less than half of highly numerate liberals were likely to get the right answer, compared to 85 percent of high-numerate conservatives.

“From a geeky scientific standpoint, this is incredible,” Peters said. But politically speaking, it’s troublesome. “What it suggests is that our political outlooks matter more than the data,” she explained, “even when the data is sitting in front of us and we have the ability to work our way through it.”


Why were the results for those with better number skills so skewed? The researchers believe that the highly numerate people worked harder on the math when a quick glance didn’t satisfy their political viewpoints. “They can use their intelligence to get the right answer,” Kahan said. “But when using their intelligence would disappoint them, they’re not doing it.” Instead, they’re taking a brief look at the numbers and accepting the answer that pleases them most: “They’re going with their gut.”

That, in and of itself, isn’t all that surprising to mathematicians. In most calculations we make, we consider context. “And in many ways, cognitively, that’s actually a very good thing,” said Jon Star, an associate professor in human development and education at the Harvard Graduate School of Education. “That’s a very productive part of the way our mind works. It makes a lot of things easier. If I had to interpret everything out of context every time I saw it, it would be a lot of work.”

In this case, though, the context is the participant’s own feelings about a polarized and personal political issue. “They read something about gun control,” Star said, “and that activates a whole lot of other ideas and beliefs about that idea.”

At that point, Star believes, the participants were no longer able to reason effectively using math. In fact, to look at the study’s results from a different perspective, nearly 60 percent of participants overall weren’t able to answer the question correctly, no matter which question they received. This suggests that proportional reasoning—a basic math skill typically introduced during middle school—is problematic to many people. (Indeed, a recent study found that American adults ranked 21st in numeracy out of 23 countries surveyed.) “We just need to work harder to get people to understand the math behind some of these interpretations we have to make,” Star said. “Because if they really understand how to do the math—and the math isn’t so taxing—then perhaps it will be less likely that the context could sway their thinking.”

Kahan argues that the solution to this problem isn’t as simple as improving math instruction. He believes that policy makers need to focus on shielding science from the sort of polarization that ultimately disables our ability to think critically. It’s one thing to have a legitimate difference of opinion. “That’s natural,” Kahan said. “That’s politics.” It’s quite another, he said, for the facts to simply get tossed out instead of serving as a shared basis for the conversation. He suggests that leaders need to begin framing policy debates in a way that disconnects them from our deeply ingrained political identities.

Kahan admits that won’t be easy. Politicians are always exploiting data for political gain, to create wedges and rally the base—a practice not likely to end anytime soon. And we don’t need to look far, obviously, to find the most recent example of this behavior.

“I think we are living the implications of this kind of research right now, with this government shutdown,” Ditto said. “It’s a fact war. There are red facts—and there are blue facts.”

Freelance writer Keith O’Brien is a former staff writer for the Globe and the author of the book “Outside Shot,” chronicling one town’s lonely quest for basketball greatness. E-mail him at