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The phrase "a broad consensus that" is correct and usable in written English.
It can be used when discussing a general agreement or shared opinion among a group of people regarding a particular issue or topic.
Example: "There is a broad consensus that climate change is a pressing global issue that requires immediate action."
Alternatives: "a general agreement that" or "a widespread agreement that".
Exact(60)
The Saudi strategy also risks breaking a broad consensus that has served OPEC well since the 1998 oil crisis, when prices collapsed.
There is a broad consensus that when used appropriately, respiratory depression from opioid analgesics is a rarely occurring side effect.
There is a broad consensus that Jews are well integrated.
From the 1960s there had been a broad consensus that higher education should expand.
"There's a broad consensus that Mexico needs to raise more money in taxes".
There is a broad consensus that we need a correction in education reform in the District.
Once his candidacy proved viable there was a broad consensus that it should not be normalised.
There is a broad consensus that the United States should expand its current preschool programs, particularly for disadvantaged students.
But there is a broad consensus that the Federal Reserve will be pushing up short-term interest rates very soon.
I think at this point what you find in the Israeli polity is a broad consensus that transcends party.
In short, there is a broad consensus that, from the state's point of view, the new policy is a failure.
More suggestions(15)
a broad concept that
a broad theme that
a broad responsibility that
a broad church that
a broad field that
a broad policy that
a broad valley that
a broad collection that
a broad approach that
a broad spectrum that
a broad range that
a broad knowledge that
a broad category that
a general consensus that
a broad band that
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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