If a majority of the votes cast by the electors within the boundaries of the land described in the petition are "Improvement–Yes," and if a majority of the votes cast by the electors in the district at large are "Improvement–Yes," then, but not otherwise, the board shall construct the improvement. The cost of construction shall be apportioned by the board to the lands within the boundaries described in the petition, so that each acre of irrigable land therein shall be assessed and required to pay the same amount. In all other respects the assessment and its levy and collection shall be, as nearly as practicable, in accordance with the assessment, levy and collection of other assessments and taxes levied upon lands within the district.