Jamieson, Fausset and Brown on Judges 11:10-11

10-11. the elders of Israel said unto Jephthah, The Lord be witness between us--Their offer being accompanied by the most solemn oath, Jephthah intimated his acceptance of the mission, and his willingness to accompany them. But to make "assurance doubly sure," he took care that the pledge given by the deputies in Tob should be ratified in a general assembly of the people at Mizpeh; and the language of the historian, "Jephthah uttered all his words before the Lord," seems to imply that his inauguration with the character and extraordinary office of judge was solemnized by prayer for the divine blessing, or some religious ceremonial.