Kiddushin 79A

– שניהם נותנים גט. ואם רצו ⁠– אחד נותן גט, ואחד כונס.

both men who might have betrothed her give her a bill of divorce in order to render her permitted to marry someone else. And if they wish and agree between them, one gives a bill of divorce and the other marries her.

וכן האשה שנתנה רשות לשלוחה לקדשה, והלכה וקדשה את עצמה, אם שלה קדמו ⁠– קדושיה קידושין, ואם של שלוחה קדמו ⁠– קידושיו קידושין. ואם אינן יודעין ⁠– שניהם נותנים לה גט, ואם רצו ⁠– אחד נותן לה גט ואחד כונס.

And similarly, with regard to a woman who authorized her agent to betroth her and she then went and betrothed herself to someone else, if her own betrothal preceded that of the agent, her betrothal is a valid betrothal, and if that of her agent preceded hers, the agent’s betrothal is a valid betrothal. And if they do not know whose betrothal came first, both men who may have betrothed her give her a bill of divorce. And if they wish, one may give a bill of divorce and the other marries her.

גמ׳ וצריכא, דאי אשמעינן גבי דידיה, משום דגברא קים ליה ביוחסין, אבל איתתא דלא קים לה ביוחסין, אימא לא ניהוו קידושיה קידושין.

Talmud: And it is necessary to state this halakha with regard to one who betroths his daughter as well as with regard to a woman who betroths herself. As had the Mishnah taught us this halakha only with regard to the father himself, one might say that it is because a man is expert with regard to lineage, and his decision to betroth his daughter on his own after having appointed an agent must have been due to the superior lineage of the man that he found willing to marry her. But with regard to a woman, who is not expert with regard to lineage, one might say her betrothal should not be considered a valid betrothal, as she still intends for her agent to be able to accept betrothal for her from a man with superior lineage.