What can we learn from the U.S. Supreme Court’s landmark decision legalizing gay and lesbian couples nationwide? In a time when the two political parties seem more bitterly divided than ever, this case has a clear message: People can change their deeply held beliefs. Persuasion is possible.

In making their decision, the Court had to decide whether gay marriage supporters wanted to change the institution of marriage or join it. The majority opinion, written by Justice Anthony Kennedy, leaves no doubt about where they came out.

A decade ago, when equal marriage first became law in just one state, Massachusetts, opponents argued gay marriage profoundly would change — and weaken — the institution of marriage. Vast numbers of Americans agreed, and state constitutional amendments and other laws banning gay marriage were passed in state after state.

To build toward their hoped-for ultimate goal, a national victory for equal marriage at the Supreme Court, gay marriage movement leaders knew they needed to turn the tide at the ballot box and create a national shift in public opinion. They did.

To understand how, consider the persuasive power of 90-year-old Harlan Gardner. When this World War II veteran from Machias appeared on television on behalf of same-sex couples being able to marry, he told listeners, “marriage is too precious a thing not to share.” In the ad, Gardner, a World War II veteran who was married for 59 years, sat at the dinner table with four generations of his family, including his lesbian granddaughter, Katie, and her partner. After Harlan said he was proud of them, his 30-year-old granddaughter replied, “we’re proud of you.”

“In my lifetime I’d really like to see Katie and Alex get married legally,” Harlan’s wife of 59 years, Dorothy Gardner, added. Harlan Gardner closed by saying, “this isn’t about politics. It’s about family and about how we as people treat one another.”

The ad featuring the Gardners was part of the 2012 Maine marriage referendum campaign. Successes in four states — Maine, Washington, Maryland and Minnesota — that year propelled the marriage movement, showing there was enough popular support for same-sex marriage to win at the ballot box.

Those victories marked a sea change from years of prior defeats and mixed results. How did they happen? In research we conducted, we found the pro-equal marriage campaigns were able to persuade voters by clarifying that gay and lesbian people didn’t just seek the legal rights that go with marriage but wanted the same love and commitment from marriage as straight people. Most importantly, those winning campaigns put straight allies front and center. They spoke about their personal journeys to accept marriage for LGBT couples.

Of course, the gay rights movement, including the push for marriage, would not have moved forward without gay activists and leaders doing everything from protesting in the streets to campaigning to filing and arguing cases in court. Many thousands, if not millions, of personal decisions to come out to family members and friends and co-workers mattered. But the massive social and political transformations that culminated in the Supreme Court’s decision also depended on straight allies sharing their stories and accepting the fact that, as Kennedy wrote, LGBT people “respect” the institution of marriage.

In Maine, one straight man spent months going door to door, telling those who would listen about a close friend, who was gay, and asking, “why shouldn’t he be able to marry the person he loves?” That canvasser and others would ask the people they met if they knew anyone gay. When they were told about an uncle or niece or neighbor, they would engage in a dialogue about that individual’s relationship. When the person at the door was an older Catholic woman, she would be asked to think about what marriage meant to her and to apply the Golden Rule. Gay canvassers would talk about their own lives and loves. Altogether, about 22 percent of the hundreds of thousand contacted in the 2012 Maine campaign changed their minds.

Instead of avoiding ideas that resonated with opponents of marriage equality — family values, religious freedom and traditional marriage — pro-gay rights campaigns adopted them.

Across the country from Harlan Gardner, a Seattle couple of 29 years, the Rev. Rich Lang and his wife, Cathy, told their story in another ad.

“I struggled with the notion of same-sex marriage, and it was compassion that broke in,” Lang said. “My shift came when I realized that, at the very core of my Christianity is the compassion that God has shown toward me.” His wife then said, “for a couple to be able to take their vows before friends and family, it means they’re together forever. And don’t we want that for everybody?”

Marriage equality campaigns activated empathy and created connections between citizens. Straight and gay speakers alike testified — often with heartfelt emotion — that marriage means the same thing for everyone. Regardless of sexual orientation, marriage is an expression of love and commitment. Same-sex marriage was presented as means for gay and lesbian couples to join the institution of marriage, not, as opponents charged, change it. And straight allies described their own journeys to accepting same-sex marriage, thus providing themselves as models with whom other straight individuals could identify.

The remarkable progress marriage equality has made in a very short time is evidence that, even in a polarized and divisive political climate, change can happen. But persuading others to change their minds requires us to find shared language and common ideas — and to talk directly to voters who are outside of our current camp. Often, both parties today seem to write off dialogue and persuasion. They see winning elections as a question only of mobilizing bases.

Real progress requires more courage than that. It took courage for marriage equality advocates to engage in deeply personal dialogue with those who might never come around to their side. Just as importantly, it took courage for straight Americans including the Gardners and the Langs to admit their thinking has evolved and to express support for ideas they have come to believe transcend one’s sexual orientation: commitment, devotion, family and love. The movement for equal marriage had no choice but to find a persuasion and dialogue strategy that took them far beyond the “base” of gay, lesbian, bisexual and transgender Americans. The Democratic and Republican coalitions are far larger — and less likely to see the need for such courage. But our republic would be better off if they did.

Amy Fried and Robert Glover are professors of political science at the University of Maine and members of the Scholars Strategy Network. This piece originally appeared on Talking Points Memo.