Then the researchers asked the subjects in each group whether they supported the Tea Party. The share that did was a small minority in both groups. Among the 255 white subjects, though, those in the group that had seen the darkened portrait were almost twice as likely to say they supported the movement.
Among the 101 participants of other races or ethnicities, by contrast, those who saw the lightened image of Obama were twice as likely to support the Tea Party as those who saw the darkened image. Because they had fewer subjects of colour, Willer and his colleagues couldn't rule out the possibility that this difference between the randomly assorted groups was due to chance.
The result suggests that some white Americans are more likely to oppose Obama solely because of the shade of his skin. For them, the reality that someone with a dark complexion occupies the nation's highest office could be a source of unease.
Past polls and experiments have also suggested that the president's race has motivated opposition to his policies.
For example, psychologist David Sears and political scientist Michael Tesler found that many white voters were willing to support white liberal politicians such as President Clinton and Secretary of State John Kerry when they were candidates for president, but voted against Obama. Since Clinton, Kerry and Obama all espoused a similar ideology, the pair surmised that Obama must have been less popular because he is black.
Conservative politicians also seemed to respond to racial animosity towards the president. A study last year found that -- intentionally or not -- some negative advertisements aired against Obama in 2008 showed him with darker skin.
Willer, though, was able to demonstrate the connection between Obama's skin colour and conservative opposition experimentally. The researchers also conducted a few more studies to see whether Tea Party support might be motivated by signs that the position of white Americans as a privileged majority is declining.
The researchers presented two groups of subjects with apparently innocuous reports about US demographic trends and the white share of the population. One group read a report that showed population data only from 2000 to 2020, making it appear that the white majority remains relatively stable. The other group read a report that showed the trend since 1960 and predictions through 2060, forecasting that the white population would decline into a minority.
Again, there were significantly greater levels of white support for the Tea Party among those who read the second report, which focused on the declining white population. Those who read that report rated their level of support for the Tea Party at an average of 1.62 points on a five-point scale, where a score of 5 signified "a great deal" of support.
Those who read the first report, showing that the white majority was relatively stable, rated their support at an average of 1.28 points. Again, supporters of the Tea Party were in the minority in both groups.
Willer and his collaborators repeated the experiment, this time with fictional economic data. In one report, the incomes of ethnic minorities were in decline, while white incomes were unchanged. In the second report, white incomes were declining while other groups' incomes did not change.
In fact, incomes for all racial and ethnic groups have declined in tandem in recent years, with no one group gaining or losing relative to the others.
Yet Willer had a hunch that because white incomes have declined, some of the white participants in the experiment might feel that white households are losing their relative advantage in the US economy. If so, the second report he showed them would have seemed to corroborate this mistaken perception.
Previous research has shown that white Americans tend to see the trend towards racial equity as a kind of competition, in which one group's loss must be another group's gain. In particular, research shows, economic distress can exacerbate racial biases, since they give members of the dominant group the mistaken impression their relative position is endangered. White Americans get "the sense that they have a shrinking piece of a pie that is itself shrinking", Willer explained.
With the second report, Willer and his colleagues showed that their subjects reinforced this unconscious bias and produced greater levels of white support for the Tea Party: Those who saw that report rated their support for the Tea Party at an average of 1.45 points. Those who saw the first report, showing incomes for racial minorities declining, rated their support at an average of 1.23 points.
This kind of zero-sum thinking doesn't seem common among racial minorities. If it were, then one would expect that minorities who read the first report -- showing their disadvantage increasing -- would be more likely to oppose the Tea Party as a protest against white privileges.
On the contrary, participants of colour who saw the report that emphasised declining white economic status were more likely to oppose the Tea Party. Again, this difference might have been the product of random chance.
Willer started this series of experiments in 2011. He was already wrapping up the research when Trump announced his presidential campaign by calling Mexican immigrants criminals, so he doesn't have direct evidence on whether racial biases have contributed to Trump's success. Yet other research, including polling by the Washington Post, suggests that some white voters' perception that their dominance as a racial group is threatened has motivated some to cast ballots for the presumptive Republican nominee.
"A lot of analysts have been shocked to see a major party candidate receive so much popular support despite a track record of controversial statements toward multiple ethnic groups," Willer said. "It's less surprising if you think of the Tea Party as a sort of historical bridge to the Trump candidacy."
The movement, he explained, might have made using the kind of inflammatory rhetoric that Trump has employed more socially acceptable, and past research suggests that the movement could have created a new sense of racial identity among its supporters.