Winning hearts and minds — the Bush administration, foreign-policy wonks, even the U.S. military agree that this is the key to any victory over global terrorism. Yet our public diplomacy program has made little progress toward improving America's image. Few seem to recognize that American ignorance of Islam and Muslims has been the fatal flaw.

How much do Americans know about the views and beliefs of Muslims? According to polls, not much. Perhaps not surprising, the majority of Americans (66 percent) admit to having at least some prejudice against Muslims; 1 in 5 say they have "a great deal" of prejudice. Almost half do not believe American Muslims are "loyal" to this country, and 1 in 4 do not want a Muslim as a neighbor.

Why should such anti-Muslim bias concern us? First, it undermines the war on terrorism: Situations are misdiagnosed, root causes are misidentified and bad prescriptions do more harm than good. Second, it makes our public diplomacy sound like double-talk. U.S. diplomats are trying to convince Muslims that the United States respects them and that the war on terrorism is not out to destroy Islam. Their task is made infinitely more difficult by the frequent airing of anti-Muslim sentiment on right-wing call-in radio, which is then heard on the Internet.

Finally, public ignorance weakens our democracy at election time. Instead of a well-informed citizenry choosing our representatives, we are rendered vulnerable to manipulative fear tactics. We need look no further than the political attacks on Barack Obama. Any implied connection to Islam — attending a Muslim school in Indonesia, the middle name Hussein — is wielded to suggest that he is unfit for the presidency and used as fuel for baseless rumors.

Anti-Muslim sentiment fuels misinformation and is fueled by it — misinformation that is contradicted by evidence.

Starting in 2001, the research company Gallup embarked on the largest, most comprehensive survey of its kind, spending more than six years polling a population that represented more than 90 percent of the world's 1.3 billion Muslims. The results showed that much of the conventional wisdom about Muslims — views touted by U.S. policymakers and pundits and accepted by voters — is false.

For instance, Gallup found that 72 percent of Americans disagreed with this statement: "The majority of those living in Muslim countries thought men and women should have equal rights." In fact, majorities in even some of the most conservative Muslim societies directly refute this assessment: 73 percent of Saudis, 89 percent of Iranians and 94 percent of Indonesians say that men and women should have equal legal rights. Majorities of Muslim men and women in dozens of countries also believe that a woman should have the right to work outside the home at any job for which she is qualified (88 percent in Indonesia, 72 percent in Egypt and 78 percent in Saudi Arabia) and to vote without interference from family members (87 percent in Indonesia, 91 percent in Egypt, 98 percent in Lebanon).

What about Muslim sympathy for terrorism? Many charge that Islam encourages violence more than other faiths, but studies show that Muslims are at least as likely as Americans to condemn attacks on civilians. Polls show that 6 percent of the American public thinks attacks in which civilians are targets are "completely justified." In Saudi Arabia, this figure is 4 percent. In Lebanon and Iran, it's 2 percent.

Moreover, it's politics, not piety, that drives the small minority — just 7 percent — of Muslims to anti-Americanism at the level of condoning the attacks of Sept. 11, 2001. Looking across majority-Muslim countries, Gallup found no statistical difference in self-reported religiosity between those who sympathized with the attackers and those who did not. When respondents in select countries were asked in an open-ended question to explain their views of the Sept. 11 attacks, those who condemned it cited humanitarian as well as religious reasons. For example, 20 percent of Kuwaitis who called the attacks "completely unjustified" explained this position by saying that terrorism was against the teachings of Islam. A respondent in Indonesia went so far as to quote a verse from the Quran prohibiting killing innocents. On the other hand, not a single respondent who condoned the attacks used the Quran as justification. Instead, they relied on political rationalizations, calling the United States an imperialist power or accusing it of wanting to control the world.

If most Muslims truly reject terrorism, why does it continue to flourish in Muslim lands? What these results indicate is that terrorism is much like other violent crime. Violent crimes occur throughout U.S. cities, but that is no indication of Americans' general acceptance of murder or assault. Likewise, continued terrorist violence is not proof that Muslims tolerate it. Indeed, they are its primary victims.

Still, the typical American cannot be blamed for these misperceptions. Media-content analyses show that the majority of U.S. TV news coverage of Islam is sharply negative. Americans are bombarded with news stories about Muslims and majority-Muslim countries in which vocal extremists, not evidence, drive perceptions.

Rather than allow extremists on either side to dictate how we discuss Islam and the West, we need to listen carefully to the voices of ordinary people. Our victory in the war on terrorism depends on it.

John L. Esposito is an Islamic-studies professor at Georgetown University; Dalia Mogahed is executive director of the Center for Muslim Studies at Gallup. They wrote this commentary for the Los Angeles Times.