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The phrase "a simple majority of" is correct and usable in written English.
It is typically used in contexts involving voting or decision-making, where more than half of the votes or members are required to achieve a particular outcome.
Example: "The proposal was approved by a simple majority of the members present at the meeting."
Alternatives: "an absolute majority of" or "a bare majority of".
Exact(58)
A simple majority of MPs is needed.
A simple majority of 17 wins the election.
A simple majority of 51 votes is needed to win.
The deal needs ratification by a simple majority of the 30 teams and a simple majority of the 430-plus players.
Ratification requires a simple majority of the owners of the N.B.A.'s 30 teams and a simple majority of the 430-plus players.
Only a simple majority of board members is required to allow an execution to proceed.
leaders have been chosen more by general acclamation than by a simple majority of the votes.
A simple majority of its 11 members is enough to start an investigation.
Under the current process, passage of citizen-proposed amendments requires a simple majority of voters.
A simple majority of votes was required for the guild to certify the three-year deal.
That is a simple majority of the 4,334 delegates who will attend.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com