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"based on two criteria" is a correct and usable phrase in written English.
It can be used to describe the process of making a decision, evaluating a situation, or making a judgment after taking two criteria into consideration. For example, "The admission committee selected the final candidates based on two criteria: academic performance and extracurricular activities."
Exact(60)
The research considered family types based on two criteria.
The authors have created a measure of the sophistication of an economy based on two criteria.
Development International's ranking was based on two criteria: whether companies offered a disclosure, and whether their disclosure mentioned efforts to prevent forced labor in their supply chain.
The BBC decides eligibility for party political broadcasts, which run outside elections, based on two criteria: representation, such as seats in the the Commons or European parliament; and an assessment of electoral support.
The choice of numeric weights is based on two criteria.
Judges voted based on two criteria: cuisine and style/decor/service (as a single category).
This new population is sorted based on two criteria: (1) rank and (2) crowding distance.
Then, a next-hop host is selected within this equivalent class based on two criteria: Criterion 1.
The scenarios were chosen based on two criteria: Based on participant voting, the scenarios were prioritized based on the votes received from participants.
The methods in this approach extract facts based on two criteria: the existence of a numeric attribute and/or the cardinality of the association between entities.
The 43 innovations identified were categorized based on two criteria: level of specificity (general, recognizable, branded) and type of change (pedagogical, content, both, neither).
More suggestions(18)
based on two approaches
based on two requirements
based on two concerns
based on two indexes
based on two measurements
based on two thresholds
assessed on two criteria
based on two benchmark
based on two evidence
based on two standard
based on several criteria
based on two adults
based on two ideas
based on two propositions
based on two sets
based on two arguments
based on two axioms
based on two surveys
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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