Immediately after Proposition 8 passed, many who supported same-sex marriage tried to make sense of the results. A set of assumptions gained wide acceptance. Some are correct. Most, however, are just plain wrong. And it’s crucial that we know what happened in the last election before launching another attempt to legalize marriage for all.

I recently headed a team that analyzed data from polls conducted by the No on 8 campaign during the run-up to the election. Our analysis sheds new light on what fueled the Proposition 8 victory.

One big question after the election: Who moved? Six weeks before the vote, Proposition 8 was too close to call. But in the final weeks, supporters pulled ahead, and by election day, the outcome was all but certain.

After the election, a misleading finding from exit polls led many to blame African Americans for the loss. But in our new analysis, it appears that African Americans’ views were relatively stable. True, a majority of African Americans opposed same-sex marriage, but that was true at the beginning and at the end of the campaign; few changed their minds in the closing weeks.

The shift, it turns out, was greatest among parents with children under 18 living at home — many of them white Democrats.

The numbers are staggering. In the last six weeks, when both sides saturated the airwaves with television ads, more than 687,000 voters changed their minds and decided to oppose same-sex marriage. More than 500,000 of those, the data suggest, were parents with children under 18 living at home. Because the proposition passed by 600,000 votes, this shift alone more than handed victory to proponents.

Perhaps it shouldn’t be a surprise. The Yes on 8 campaign targeted parents in its TV ads. “Mom! Guess what I learned in school today!” were the cheery-frightening first words of the supporters’ most-broadcast ad. They emerged from the mouth of a young girl who had supposedly just learned that she could marry a female when she grew up.

Among the array of untrue ideas that parents could easily take away: that impressionable kids would be indoctrinated; that they would learn about gay sex; that they would be more likely to become gay; and that they might choose to be gay. California voters, depending on where they lived in the state, were exposed to the Yes on 8 ads 20 to 40 times.

The lesson: It’s not enough to make the case for same-sex marriage. It’s also important to arm voters — particularly parents — against an inevitable propaganda attack. And it’s crucial to rebut lies so parents don’t panic.

Another misconception was that those who voted for Proposition 8 were motivated by hate. This does not describe most of the 687,000 who changed their minds in the closing weeks. After all, they supported same-sex marriage before the opposition peeled them away. Yes, they turned out to be susceptible to an appeal based on anti-gay prejudice. But they were frightened by misinformation. No on 8’s one TV ad that directly responded to the fear-mongering helped assuage some of the fear, but it was too little, too late.

One final false assumption by same-sex marriage supporters was that the election was so close that it will be easy to pass same-sex marriage the next time out.

It’s true that the official election results — 52% to 48% — appeared quite close. But the truth is more complicated. The data we analyzed show that the No on 8 campaign benefitted from voter confusion.

Polling suggests that half a million people who opposed same-sex marriage mistakenly voted against the proposition. They were confused by the idea that a “no” vote was actually a vote for gay marriage. This “wrong-way voting” affected both sides, but overwhelmingly it helped the “no” side. Our analysis suggests that the division among California voters on same-sex marriage at the time of Proposition 8 was actually 54% to 46% — not so close. We are actually 1 million votes away from being able to reverse Proposition 8.

This analysis makes absolutely clear that supporters of same-sex marriage have a lot of work to do before we return to the ballot. But that work is already underway, and now real knowledge can underpin our efforts.

David Fleischer heads the LGBT mentoring project, which is now part of the Los Angeles Gay and Lesbian Center’s new leadership program Learn Act Build. The project’s full report and data can be viewed at prop8report.org.