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'.

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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?
Which is right:A majority of class prefer/prefers dress code?
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You need a couple of articles in there: "A majority of the class prefer/prefers a dress code."

Have you read the previous comments? There is no one right answer to your question. You will hear both, at least in America. But I would say "prefers", probably by attraction to "class". Thing is, I am an American, and we construe words like "class" and "team" as singular (a Brit would say "prefer" given the same reason). You might also hear "prefer" in America from people who observe strict grammar and construe "majority" as plural.