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Promiscuity or promiscuousness: having or characterized by many transient sexual relationships; demonstrating or implying an undiscriminating or unselective approach; indiscriminate or casual; adulterine or libertine; epicene.
It's considered the opposite of chastity, and may be reclaimed by polyerosous, or otherwise nonmonoerosous, individuals. Note that some use this in a moralist way through condemning glances.