We are learning Mishnah 7 of the third chapter of Maseches Kiddushin, which deals with a father who testifies that he betrothed his daughter but does not know to whom.
"Kidashti es bitti ve'eini yodea l'mi kidashtiha, u'va echad ve'amar ani kidashtiha - ne'eman": "I betrothed my daughter and I do not know to whom I betrothed her, and one man came and said: I betrothed her - he is believed."
The betrothal of a daughter is in the hands of her father, and this right belongs to him as long as she is a minor or a na'arah. In our case the father testifies that he did indeed betroth his daughter, but he does not remember to whom. A man comes and claims: I am the one who betrothed her - and the Mishnah rules that he is believed.
The scope of this man's credibility:
Believed regarding a get: If he were believed only to give her a get and thereby permit her to marry anyone, that would be self evident, based on the principle "a person does not sin when there is nothing in it for him" - we do not assume that a man will lie and sin where he gains nothing himself and merely helps someone else. After all, what motive would he have to come forward and permit her?
Believed even to marry her: The Gemara explains that his credibility is not limited to that; he is believed even to marry her in practice. The reason is this logic: if he were not the man who betrothed her, he would not dare to tell the father "I betrothed her," out of fear that the father would look at him and say: one thing is clear to me - it was not you. Because of that very fear, we may believe him and establish that he is indeed the husband.
"Zeh omer ani kidashtiha v'zeh omer ani kidashtiha": "This one says: I betrothed her, and this one says: I betrothed her."
When two men each claim that he is the one who betrothed her, the Mishnah rules: "shneihem nosnin get" - both of them give a get. We do not assume that both are lying; rather, one of them is the true husband and the other is lying, and since we do not know which is which, both give a get, and thereby she is permitted.
"V'im ratzu - echad nosen get v'echad kones" - and if they wish, one gives a get and the other marries her. Once one of them has given his get, we may assume that the other is the true husband, and therefore he may marry her.
In summary: In this Mishnah we learned that when a father betrothed his daughter and does not know to whom, and a man comes and claims "I betrothed her," he is believed - and not only to give a get, based on "a person does not sin when there is nothing in it for him," but even to marry her, since he would not have dared make such a claim in front of the father. And when two men make this claim, both give a get, and if they wish, one gives a get and the other marries her.