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The phrase "a collective problem" is correct and usable in written English.
It can be used to describe an issue that affects a group of people or a community as a whole.
Example: "Climate change is not just an individual concern; it is a collective problem that requires global cooperation to address."
Alternatives: "a shared issue" or "a communal challenge".
Exact(23)
Climate change is a collective problem, which can be dealt with only collectively.
"It's a collective problem," he said.
It's not all about Marler – it was a collective problem.
It's a collective problem," Ms. Thomas-Blate said.
The recession in the euro zone "is a collective problem," he said.
Leyland said the loss was a collective problem, and it was.
Similar(37)
Therefore, mapping the designed roles of related cognitive components in a group discussion may develop group cognition in a collective problem-solving process.
Therefore, while widespread access to height enhancements will potentially lead to a collective action problem, this problem might be somewhat limited in scope (due to the fact that height does not appear to confer a wellbeing advantage on women) and in magnitude (due to the fact that increasing height is likely to cause a net loss of wellbeing at some point).
However, it is often very difficult to observe a system of collective problem solving by observing every individual action.
This problem is known as a collective action problem.
Interactive disaster planning also consolidates a community's commitment to collective problem solving, and nurtures long-term capacity for a DRR plan's implementation and future review.
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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