Abu Ishaq says: Abu al-Safar and I went to Abu Ja'far, and I asked about a man who gave his wife the choice and the wife chose herself. He said: It is one divorce, and her husband has more right to take her back. We said: And if the woman chooses her husband? He said: Then nothing at all is due from him. We said: People narrate from Ali (may Allah be pleased with him) that if the woman chooses her husband, it is one divorce and the husband has more right to take her back; and if the woman chooses herself, it is one separating (irrevocable) divorce and the woman has more control over herself. He said: That is something they found in written pages. As for Abdullah bin Mas'ud (may Allah be pleased with him), what is authentic from him we have already mentioned.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الخلع والطلاق / 15032