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The phrase "allocated a lesser" is correct and usable in written English.
It can be used in contexts where resources, responsibilities, or roles are distributed in a way that one is given a smaller amount or lower status compared to others.
Example: "In the recent budget review, the department was allocated a lesser amount than last year, which has raised concerns about our ability to meet project deadlines."
Alternatives: "assigned a smaller" or "designated a lower".
Exact(1)
Although the PAL concept was rated to be a good learning method (LS 1.8), student-teachers were allocated a lesser level of competence than staff lecturers (p < 0.001).
Similar(59)
There are suggestions that LIC governments allocate a lesser percentage of their annual domestically generated budget resources to health than they should, and could afford.
However, if the two arms had already been allocated a different number of units then the greater number of units would be automatically allocated to the lesser recruited treatment arm.
Each actor is allocated a dressing room.
And was then allocated a middle seat.
Abedi was allocated a red dot.
They are allocated a lane each.
The President is allocated a personal usher.
All participants were allocated a trial number.
His testimony helped allocate a further $30m.
vm_allocate - Allocate a region of virtual memory.
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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