On These Math Problems, Smarter People Do Worse

A counterintuitive pattern shows up when people answer quantitative questions: higher numeracy can make them more likely to get politically loaded problems wrong. The effect matters because it challenges the common belief that stronger math skills automatically lead to more accurate reasoning—especially when the “right” conclusion threatens or supports a person’s ideology.

The research begins with a simple proportional-reasoning trap using a fictitious skin-cream trial. Participants see a table counting how many people improved versus worsened after two weeks. Many people jump to an intuitive shortcut: whichever group has the larger raw number of “improved” cases must be better. But the correct interpretation depends on ratios. In the cream group, roughly three times as many people improved as worsened; in the control group, about five times as many improved as worsened. That means the cream, on average, made rashes worse—even though the “improved” count looks larger at first glance.

Dan Kahan and colleagues tested this with a nationally diverse sample of 1,111 Americans. Before answering, each participant took a numeracy assessment measuring quantitative reasoning rather than advanced math. When the skin-cream question used the “cream helps” framing, accuracy rose with numeracy in the expected direction—yet the higher-numeracy participants were also more likely to avoid the intuitive mistake and select the correct proportional answer. That part looks like numeracy doing its job.

The twist comes when the same proportional table is presented with reversed column headings, flipping which conclusion is correct. Again, higher numeracy predicts higher accuracy. But the study’s real target is politics: participants were split by self-reported political affiliation and then given either a gun-control version of the fictitious study or the skin-cream version.

For the apolitical skin-cream problem, liberals and conservatives follow the same accuracy pattern—no ideological split emerges. For the gun-control problem, the split is stark. When the data imply gun-control laws reduce crime, Democrats perform well and Republicans struggle; when the data imply gun-control laws increase crime, the pattern reverses. Crucially, numeracy no longer guarantees accuracy in the “threatening” direction. Among the most numerate participants, performance is worse than it should be: they become more likely to reach the conclusion that fits their prior beliefs rather than the conclusion demanded by the numbers.

The same conditional polarization appears across other issues like fracking and global warming, and even when reasoning ability is measured through science literacy or open-minded thinking. The broader takeaway is uncomfortable: people may use quantitative skill selectively—applying it to justify what they already believe—while still feeling rational.

The discussion closes with practical ideas for reducing tribal reasoning: avoid partisan rhetoric and focus on specific local policies; cultivate curiosity so people are more willing to examine evidence that conflicts with ideology. The emphasis is on awareness and accountability, not a magic fix—because the tendency to align beliefs with one’s group is deeply rooted in social survival, and it becomes more visible in today’s high-volume online information environment.