Collocations for majority - noun

big, great, huge, large, overwhelming, significant, sizeable, solid, strong, substantial, vast
silent
The march was by the silent majority who oppose terrorism.

moral
black, white
countries which have an English-speaking white majority

ethnic

compose, constitute, form, make up
English speakers form the majority of the population.

join
He joined the majority in criticizing the government's reforms.

community, culture, group, population
language, religion
opinion, view
decision
owner, shareholder
ownership
interest, share, stake
The French company holds a majority stake in the retail chain.

in the majority
In the general population, right-handed people are in the majority.

in the majority of cases
In the vast majority of cases, customers get their money back.

big, huge, large, massive (esp. BrE), overwhelming, solid, strong, substantial
clear, comfortable, decisive (esp. BrE)
bare, narrow, slender (esp. BrE), slight, slim, small, tiny (esp. BrE)
razor-thin (AmE), wafer-thin (BrE)
160-seat, etc.
two-to-one (BrE), two-thirds, etc.
absolute, outright, overall
Although they are the biggest single party, they don't have an outright majority.

popular
simple
working (esp. BrE)
To govern effectively, he will need a working majority in Congress.
the first Labour government with a clear working majority in the House

electoral
legislative (esp. AmE)
parliamentary
government (BrE)
Labour, Republican, etc.
necessary

carry, command, have, hold
achieve, capture, gain, garner, get, obtain, secure, win
They failed to win the requisite two-thirds majority.

build
If the Republicans want to build a majority, they need the north-east.

increase
Republicans increased their majority in both the House and the Senate.

defend (BrE), maintain, retain
lose
overturn (esp. BrE)
indicate, show

government, rule
leader, whip
party
decision
vote, voting (esp. BrE)
support
position, status
control

by a majority
They won by a huge majority.

majority against
Latest opinion polls have a comfortable majority against the reform.

majority in
a majority in the Senate

majority in favour/favor of
Opinion polls indicated a two-thirds majority in favour/favor of ratification of the treaty.

majority over
He has a decisive majority over his main rivals.