i found both singular and plural usages in a google search. are both acceptable?
I think it should be plural, but I don't understand why there are so many usages in singular form on the Internet.

Grammatically 'a majority' is in fact singular (the plural is 'majorities'); however, it is de facto more frequently used with plural verbs, presumably because we are usually thinking of the numbers of components-- voters or customers or whatever-- in the majority. Both acceptable.

I find the same logical vagueness with 'a number of'.

Ain't English great!
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Both are acceptable and you can use both in basically the same sentence. But if you are going to use a noun before the verb you should use the singular tense, without a noun you should use plural. I know it's confusing, even for an american, just use what comes natural.
The majority of voters prefer...
the majority prefers...
'Some people like lambchops but the majority prefer/prefers beefsteak.' Which form of the verb would you choose, Rubble?