Same-sex marriage is often lumped in with all the other social and political issues that seem to draw a schism between voters on the left and right in the U.S. But a new study shows that that line isn’t as deeply drawn as it might seem. Apparently, a single conversation on same-sex marriage with a gay or lesbian person can shift opposing viewers so strongly that a person's new stance holds a year later.

The Los Angeles LGBT Center teamed up with researchers at the University of California, Los Angeles, and had more than 12,000 one-on-one conversations with voters in Southern Californian neighborhoods that had overwhelmingly voted for a ballot measure, Proposition 8, that took away same-sex couples' ability to get married in the state.

The Center’s “volunteer canvassers accomplished what would have otherwise taken five years at the current rate of social change,” Dave Fleischer, the director of the Center’s Vote for Equality and Leadership LAB programs, said in a statement. “How did we do it? Our team had heartfelt, reciprocal and vulnerable conversations on the doorsteps of those who opposed marriage for same-sex couples, and volunteers who were LGBT came out during their conversations.” The results were published in Science.

But the crux was the canvasser’s personal involvement: Volunteers who came out as gay or lesbian and professed a desire to get married produced a more dramatic, more lasting change in the voters. Straight canvassers who just spoke of a friend or relative were less effective—they produced a slight temporary change, but the voter’s opinion reverted after a month, reports Mother Jones.

The change was also one that could make a difference. By using an online survey to assess the canvassed voter’s response to same-sex marriage, the researchers observed a percentage move roughly equivalent to the difference between voters in Nebraska or Ohio and those in Connecticut or Massachusetts. "[T]he canvassing treatment in effect transformed Midwesterners into New Englanders," the study authors write.

Even housemates of the voters the volunteers spoke to showed a shift in their stance. And the shift also included these voters’ views on LGBT people in general, not just the same-sex marriage issue. The message is one of hope, writes Lynn Vavreck for the New York Times. "Sharing, listening and showing vulnerability can change beliefs about public policy."