In a case in which a husband's "defect" was not discovered before marriage, a wife can claim that if she would have had previous knowledge of the "defect", she would not have married him. The betrothal, therefore; is considered a mistaken transaction and can be annulled without the need for a get. This argument was proposed for certain specific cases as early as the 13th century. The well-known and universally accepted halakhic authority, Rabbi Moshe Feinstein (author of Iggerot Moshe Responsa), freed women based on this argument. Among the "defects" that could lead to a decision that the betrothal was a mistaken transaction we can include: the husband infertility, mental illness, homosexuality, refusal to have children and forcing his wife to have abortions, being a pedophile, etc.
In 1996, Rabbi Emanuel Rackman established a Rabbinic Court in New York that freed women from being Agunot by annulling their marriages on the basis of the mistaken transaction argument. In addition to the above-mentioned reasons, Rabbi Rackman suggested two other types of reasons for annulling marriages: a) if a woman didn’t know that the Rabbinic Courts in our time no longer have the power to compel a get; and b) if a woman is not aware that the betrothal is a transaction by which the husband buys exclusive (sexual) rights to the woman's body. According to Rabbi Rackman, in both these cases, the wife would not have agreed to be married if she had known and understood these issues. Because this solution was applied broadly, beyond what was traditionally acceptable, most Orthodox Rabbis in the U.S. have a hard time accepting it, and do not regard such women as single. They claim that even if such a woman considers herself single, she is still married, and if she has children from another man, they will be still be considered mamzerim (bastards) according to Jewish law. Rabbinic Courts in Israel do not consider these women single either.