Any person whose application for license shall have been rejected by the Board shall have the right to appeal to a board of arbitration, which shall consist of 1 person selected by the person making the appeal, 1 person selected by the Board herein created, and these 2 to select a 3^rd person. The decision of said board of arbitration or a majority of them shall be final and binding upon all parties to said appeal. A reasonable fee toward covering the cost of arbitration shall be paid by the appellant but shall be refunded if the appellant prevails. City Code, 1976/83, art. 13, §78(b)(4) Ord. 83-931