If it appears to the board or boards of county commissioners that all portions of the drainage improvement district, joint drainage improvement district, or consolidated drainage improvement district will, as a result of the proceedings, be merged with the irrigation district or irrigation districts and that the board or boards of directors of the irrigation district or irrigation districts into which the drainage improvement, joint drainage improvement district, or consolidated drainage improvement district will be merged, which irrigation district or irrigation districts shall be named in the petition, are agreeable to the merger, and that the assent or assents thereto, in writing, by said irrigation district board or boards have been filed with the board or boards of county commissioners, the board or boards of county commissioners shall order an election to be held in the drainage improvement district, joint drainage improvement district or consolidated drainage improvement district to approve or disapprove the merger and shall fix the time thereof and cause notice to be published.