Kiddushin, Chapter Four, Mishnah Nine
Our mishnah deals with a scenario whereby a father sent an agent to betroth his daughter to a certain man and then the father betrothed her to a different man.
1) If a man gives permission to his agent to give his daughter in betrothal, and then he himself goes and gives her in betrothal to another, if his [betrothal] was first, his betrothal is valid; if the agents was first, his betrothal is valid. And if it is unknown, both must give her a divorce. And if they wish, one gives a divorce, and the other marries her.
2) Similarly, if a woman gives permission to her agent to give her in betrothal, and she goes and betroths herself [to another]: if her own preceded, her betrothal is valid; if her agents preceded, his betrothal is valid. And if they do not know, both must give her a divorce. And if they wish, one gives a divorce and the other marries her.
Section one: The ruling in this mishnah is straightforward: she is betrothed to who ever betrothed her first. Without the mishnah we might perhaps have thought that when the father sends an agent to betroth his daughter, and then he himself does that very same act, that he is in essence canceling the agents authority. Were that the case, then even if the agents betrothal came first, the daughter would be betrothed to the man the father betrothed her to. The mishnah teaches us that this is not so, and therefore whichever betrothal comes first is the betrothal that is valid.
If it is unknown which came first, then they are both potentially married to her. Therefore, both of them must divorce her, or alternatively, one may divorce her and then the other can marry her.
Section two: This halakhah is the same, but from the womans perspective. She sends out an agent to accept betrothal on her behalf and then she changes her mind and accepts betrothal from someone else. The ruling is the same as above.