Which theory of mate-selection suggests that people sift eligible mates according to specific criteria and thus reduce the pool of potential partners to a small number of candidates?

Filter theory

Explanation:

Filter theory is a sociological theory that explains how the choice of mates to date or being in a relationship with is determined by the use of certain criteria in limiting the number of potential mates they have to consider for a relationship. Criteria for selection could border around sociodemographic characteristics, similarity of attitudes or complementarity of mates.

For example, one of the examples of sociodemographic characteristics an individual may use to sift eligible mates is religion. A person may sift out mates that are not from the same religion as theirs, and restrict the choice of potential mates to those who practice the same religion with them.