The election provided herein for cases where the improvement is initiated by resolution shall be governed by the following rules: (1) All ballots must be signed by the owner or reputed owner of property within the proposed district according to the records of the county auditor; (2) each ballot must be returned to the clerk of the board not later than one week after the public hearing; (3) each property owner shall have one vote for each full dollar of estimated assessment against his or her property as determined by the preliminary estimates and assessment roll; (4) the valid ballots shall be tabulated and a majority of the votes cast shall determine whether the formation of the district shall be approved or rejected.