Crowds cheer during the Democratic National Convention in Philadelphia on July 28, 2016. (Photo by Michael Robinson Chavez/The Washington Post)

Last week, Democrats wrapped up their national convention by wrapping themselves in the American flag – a potent symbol of patriotism and national identity.

Conventions always feature flags, but this year’s display seemed part of a broader Democratic effort to claim the mantle of patriotism from Republicans. The event featured the theme of American greatness, with speeches by military leaders, veterans, and their families, and frequent “USA!” chants from the audience.

For politicians, embracing the flag seems like a no-brainer. What better way to assure voters that you have the national interest in mind than vigorous displays of patriotism?

Does flag-waving help Democrats or Republicans?

But our research suggests that flag-waving might not benefit Democratic nominee Hillary Clinton – and may even help Donald Trump and the Republican Party instead.

Republicans have frequently emphasized patriotism in contemporary presidential campaigns. For instance, George H.W. Bush in 1988 criticized Michael Dukakis for vetoing a law that would have required teachers to lead their classes in the pledge of allegiance. In 2008, Republicans questioned Barack Obama’s patriotism because he did not consistently wear a flag pin on his lapel. And in 2012, our analysis found that 43 percent of Mitt Romney’s campaign ads featured an image of the American flag, while 34 percent of Obama’s did.

This might explain why Republicans in recent decades have “owned” patriotism as a political concept, along with policy differences on military affairs and related topics. While there’s nothing inherently partisan about patriotism, voters consistently see Republican candidates as more patriotic than Democrats. And voters with traditionally patriotic attitudes tend to cast ballots for Republicans.

Indeed, a highly publicized 2011 psychology study by Travis J. Carter, Melissa J. Ferguson and Ran R. Hassin found that subjects exposed to images of the American flag were more likely to express support for the 2008 GOP presidential nominee, John McCain.

In 2012 and 2013, we designed follow-ups to that study to determine whether Democratic candidates could inoculate themselves from criticisms of their patriotism by appearing with the flag. We reasoned that pro-Republican effects might disappear if the flag provided visual evidence of a Democratic candidate’s patriotism.

But we were wrong.

Here’s how we studied this question, and what we found

In two 2012 studies run with convenience samples (one undergraduate, another Mechanical Turk), we included images of Mitt Romney and Barack Obama in election surveys. We randomly assigned some respondents to see images of the candidates with the flag, while others saw the same pictures of the candidates but without the flag. (For purposes of comparison, we also had conditions in which participants saw a flag but no candidates, and a control condition where they saw no images.)

The flag didn’t help Obama at all – in fact, it hurt him. We consistently found that any exposure to the flag slightly increased support for Romney, especially among independent-leaning Republicans, patriotic people, and those with anti-black attitudes. Other subjects were unaffected.

In other words, even when Obama appeared with the flag, it helped Romney, relative to respondents who saw Obama without the flag. In addition, support for Romney was higher in the treatments where Romney appeared with the flag than in conditions where he appeared without it.

This doesn’t appear to be peculiar to 2012. When we repeated the same experiment in 2013 featuring Joe Biden and Paul Ryan as potential 2016 presidential candidates, we got the same results.

Of course, the influence of flags is small

To be sure, the influence of flags is small and unlikely to be decisive. Since the groups affected by flag imagery are Republican-leaning, this suggests that exposure to the flag reinforces Republican loyalty among those who might be likely to waver. This probably works in tandem with other campaign events, rhetoric, and imagery.

But taken together, these flag studies indicate that Republicans would do well to wave the flag, while Democrats might want to be more cautious about using it.

At the same time, not using the flag could be problematic for Democrats, spurring Republican criticism. Indeed, Republicans criticized the first day of last week’s Democratic convention for insufficient flags on stage. Although our studies did not test the effects of criticism about the absence of the flag, we might expect these critiques to have pro-Republican effects similar to the flag itself.

One solution to this dilemma for the Democrats might be a thread-the-needle strategy: Display the flag to avoid criticism, but do so primarily with Democratic audiences less likely to be affected by it. Waving the flag at the DNC then — an event that more Democrats than Republicans would have watched — might have been part of that approach, though of course news coverage of the event exposed many non-Democrats to its imagery.

2016 might be different. Or it might not

Given the unusual dynamics of 2016, it is difficult to say how flag use will affect the current campaign. Trump’s controversial “America First” theme seems to double-down on patriotism even as he disparages sacrifices by U.S. military veterans. And perhaps Clinton hopes to make inroads with patriotic voters by emphasizing American exceptionalism and trumpeting her support for, and from, the military.

But because party images tend to be durable, overcoming the flag effects evident in our studies may take time. Until then, the Democrats may be wise to temper use of the flag in its messages to wider audiences.

Nathan Kalmoe is assistant professor of political communication in the Manship School of Mass Communication and Political Science at Louisiana State University.

Kimberly Gross is associate director and associate professor in the School of Media and Public Affairs at George Washington University.