Before any proposition for the issuance of limited liability refunding bonds, as provided for in this chapter, of an irrigation district in this state shall be submitted to the electors thereof, the board of directors of said district shall at their option have authority, upon the written consent of the owners of at least fifty-one percent of the face value of the bonds proposed to be refunded, and upon the written approval of the state department of ecology, and of the owners of fifty-one percent of the acreage of the land within the district, to institute proceedings in the superior court of the proper county to determine the irrigable acreage of the lands which shall be subject to assessment for the payment of said refunding bonds and the interest thereon, and to determine the maximum benefits to be received by said lands from said proposed refunding bonds, in the manner herein provided.