The mayor, the director of law and the director of finance shall constitute the board of revision of assessments. The mayor shall be the president of the board and the director of finance shall be the secretary thereof. It shall meet from time to time as provided by its rules, and shall hear all claims and objections as to the character of all improvements to be paid for in part or in whole by special assessment as provided in the assessment report. A majority of those constituting the board of revision of assessments shall have power to determine all complaints and objections submitted to it; and as to each improvement, the board shall, after such hearing, amend, equalize and adjust the assessment report, and shall report to the commission its findings as to the necessity for the improvement, any amendment it directs in the assessments, the estimates of benefits and allowances of damages.