Conservatives have lost the war against same-sex marriage on the two most important fronts: American law and American public opinion. Between 2003 and the 2015 Supreme Court decision legalizing gay marriage, it had become law in all but 15 states. During the same period, American public opinion shifted swiftly from solid opposition of gay marriage to swelling support.

Defeat is reality, but conceding it is not an option in the culture wars. So what is left for conservatives to do? For some, the last line of defense has been to insinuate that the American public is lying.

After a Washington Post-ABC News Poll showed that support for gay marriage reached an all-time high of 58 percent, former Republican presidential hopeful Gary Bauer declared, “the polls are skewed.” Ralph Reed, former president of the Christian Coalition added, “the idea that the American people are, you know, universally for same-sex marriage is just not backed [up].” Tony Perkins of the conservative Family Research Council made similar arguments at the time.

This theory has remerged yet again with Albert Mohler, president of the Southern Baptist Theological Seminary, asking, “What if public opinion has not actually shifted nearly as much as is claimed?” It’s not the fault of the pollsters, he says, but “it does seem certain that a majority of Americans will tell a researcher that they support same-sex marriage, even if they believed the opposite just a few years before.”

The problem with these conservative cries is that they don’t tend to cite any evidence to counter the prevailing view. But is it possible that Americans are caving to social pressure and lying to researchers about their attitudes regarding same-sex marriage? Could it be that public opinion has not shifted as much as is commonly believed? The best people to answer such questions are public-opinion experts, and most say that this conservative theory is unlikely.

The official social-science term for what conservatives are insinuating is at play is “social-desirability bias,” which is the tendency of respondents to answer sensitive questions in a manner that will cast them in the best possible light to an interviewer.

According to Robert Jones, CEO of the Public Religion Research Institute (PRRI), social desirability bias is only a risk when poll questions address an issue widely believed to have a consensus opinion and the poll involves a live human interviewer about whose opinion the respondent is worried.

“One straightforward way to test for the existence of social desirability bias is to remove the presence of the human interviewer by asking the identical question in an online survey, where the respondent is assured anonymity and answers the question in the privacy of their own home without any live human interaction,” Jones says.

In 2013, PRRI conducted two surveys in the same time period. Both utilized a random sample of adults, but one was conducted using traditional live telephone interviewing and the other was conducted online. The two surveys asked an identical question about support for same-sex marriage, but found no statistical differences between the online and telephone surveys.

“We found no evidence of social-desirability bias on the question about same-sex marriage and have no evidence that Americans are systematically lying to researchers about their true opinions,” Jones says. “This point is further supported by the convergence of findings across hundreds of surveys conducted by dozens of different polling organizations, which all point to the same thing: a real sea change in American attitudes about same-sex marriage.”

Jones is not the only religion researcher who seems skeptical of the idea that a significant number of people are lying to pollsters. Ed Stetzer of LifeWay Research notes that while cultural pressure can produce a “halo effect” that might inflate numbers in polls, “acceptance of same-sex marriage is the trend either way.” David Kinnaman of the Barna Group also acknowledges that the possibility of bias, but he also concludes “almost all the polling points to the fact that attitudes on same-sex marriage and LGBT issues are changing.”

I can only find a single study that suggests social desirability may be at work on this matter, and that study estimates the influence at about 5 to 7 percent. So conservatives’ best-case scenario would only reduce the shift in American attitudes by a nominal amount.

Another reason to doubt the notion that Americans are lying about their attitudes is the theory is the time span of the alleged shift in attitudes about same-sex marriage. In 2001, Americans said they opposed same-sex marriage by a margin of 57 percent to 35 percent. By 2015, those numbers had nearly flip-flopped, with a whopping 55 percent in support and 39 percent opposing same-sex marriage. According to Gregory Smith, associate director of research for Pew, if social desirability bias is really at work, it cannot explain the early phases of the shift, when there was not a widely held consensus opinion in favor of LGBT rights and marriage.

“Today, the majority opinion is in favor of same-sex marriage, but that wasn’t the case when we started polling on this,” Smith says. “It’s hard to understand why people would feel pressure to express what was at that time a minority opinion.”

If anything, social-desirability bias may be working in the opposite direction— acceptance of same-sex marriage may be even higher than we think.

When PRRI tested bias on the matter of same-sex marriage in 2013, it also tested church attendance. Its study showed that “Americans significantly inflate religious participation” by saying they attend church regularly when they do not. In the same way, it’s possible that Christians who quietly support same-sex marriage but were raised to believe that it is sinful might actually say they oppose it to seem more holy or moral.

“In the religious measures where we see differences,” says Jones, “the evidence suggests that the social pressure is in the direction of presenting oneself as more traditional.”

Every data set from virtually every reputable research organization points in the same direction: towards greater acceptance of same-sex marriage and rights among virtually every subset in the American population. And for some, that may be hard to accept.

“When people agree with research findings, they rarely or never question the methodology,” Kinnaman says. “However, when people don't agree with data findings, they either just ignore it or find reasons to object to the methods and questions asked.”

Many conservatives believe that American culture is, in the words of the late Daniel Patrick Moynihan, “defining deviancy down.” In their view, same-sex marriage is another example that Americans are calling what is “deviant” acceptable. Given these views, it’s understandable that conservatives would not like the trends we’re witnessing. But that doesn’t mean they aren’t real or ongoing. As Moynihan was also fond of saying, “You’re entitled to your own opinions, but you’re not entitled to your own facts.”