The phrase "a majority believe" is correct and usable in written English.
It can be used when discussing the opinions or beliefs held by a large portion of a group or population.
Example: "In recent surveys, a majority believe that climate change is a pressing issue that needs immediate action."
Alternatives: "most people think" or "the majority of individuals feel".
Other polls have shown that a majority believe that both candidates are dishonest and incapable of directing the economy out of recession.
Still, as a group, they are not overtly anti-American -- three-quarters have a favorable view of the American people and a majority believe President Obama when he says he wants to withdraw troops from the region.
Over all, 50 percent of those surveyed oppose building the project two blocks north of the World Trade Center site, even though a majority believe that the developers have the right to do so.
In striking contrast to opinion in the United States, where polls show a majority believe there was a connection between Saddam Hussein and Al Qaeda terrorists, the rest of the world remains skeptical.
As Jonathan Chait (courtesy of his Twitter buddy Robert Christian) points out, these pro-entitlement, anti-government voters fit the profile the Pew political typology calls "the Disaffecteds":Defining values: A majority believe that the government is wasteful and inefficient and that regulation does more harm than good.
Although most polls indicate that a majority believe a two-state solution is the only way to guarantee Israel's continuation as a state with a strong Jewish majority, many also feel a religious or emotional attachment to the West Bank as the country's biblical heartland.
A majority believes Britain's political system to be fundamentally flawed.
SCOTUSblog (@SCOTUSblog) #doma jurisdiction argument continues with no clear indication of whether a majority believes #scotus has the power to decide the case.
And a majority believes that the White House, emboldened by the victory in Iraq, is now more likely to consider attacking North Korea, Syria or Iran.
Violent crime in L.A. had dropped by almost fifty per cent; an unprecedented eighty-three per cent of residents approved of the job the L.A.P.D. was doing, and a majority believed the police treated all races and ethnicities fairly.
