Ibrahim (may Allah have mercy on him) says that Sayyiduna Umar and Sayyiduna Ibn Mas'ud (may Allah be pleased with them both) both used to say: When the husband gives the wife the choice and she chooses herself, it is one divorce and the man has more right to her; and if the wife chooses her husband, nothing is due from him.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الخلع والطلاق / 15025