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"an objective criterion" is a correct and usable phrase in written English.
You can use it in all situations where you need to refer to a standard or guideline for judgment that will be applied consistently, without bias or individual interpretation. For example: "In order to ensure fairness, we need to establish an objective criterion for evaluating applicants' qualifications."
Exact(59)
They regarded the contention that historical understanding presupposes an allegedly direct identification with the mental processes of past human agents as representing at best a heuristic recommendation of doubtful utility, at worst an obscurantist doctrine that transparently fails to provide an objective criterion whereby divergent historical interpretations can be evaluated.
The procedure is based on and justified by an objective criterion.
The procedure is based on and justified by an objective criterion. .
This method also allowed an objective criterion for the characterization of several bubble flow patterns.
A simple method to detect audible echoes is proposed as an objective criterion for room acoustics.
Vinet's measure (correct classification rate) is used as an objective criterion to compare the behavior of the different criteria.
The Mohists justify their consequentialist ethics by appeal to the intention of Heaven (Tian), which they believe provides an objective criterion of morality.
Dewey holds that Barnes has set forth an objective criterion of value in paintings which will eventually allow for adequate psychological analysis of aesthetic experience.
Nietzsche only makes the remarks that seem to suggest that power is an objective criterion in passages from the Nachlass, work that Nietzsche never published during his lifetime.
The design of the polarimeter was based on an objective criterion that allowed to optimize the accuracy of the measurements.
Similar(1)
He said insurance companies had long differentiated between men and women in calculating risk because they considered gender differences to be an "objective criteria".
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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