Within 30 days after the approval of the petition and report, the county commissioners or county council shall call a meeting of the landowners to elect a board of managers. At least 10 days before the meeting, the county commissioners or county council shall post a notice of the meeting at four public places in the area or vicinity of the area of the drainage association. The notice shall state the time, place, and purpose of the meeting. Each landowner is entitled to vote in the election of the board of managers until the board of viewers report is approved by the county commissioners or county council. When the report of the board of viewers is approved, each landowner is entitled to vote according to the special assessment on the landowner shown in the report as follows: for any special assessment not exceeding $15, one vote; for any special assessment more than $15 and not exceeding $35, two votes; for any special assessment more than $35 and not exceeding $60, three votes; for any special assessment more than $60 and not exceeding $100, four votes; for any special assessment more than $100, one additional vote for each $50 in excess of $100, plus one additional vote for any remaining part less than $50. Any landowner may vote by written proxy signed by the landowner. A quorum consists of the number of landowners who are entitled to cast a majority of all the votes as provided in subsection (c) of this section. On proof that notice has been given as required in subsection (b) of this section, if a quorum is not obtained, the county commissioners or county council shall appoint the managers. The board of managers elected under subsection (a) of this section shall determine by a random drawing the managers who: serve until the date of the first regular annual meeting; serve until the date of the first regular annual meeting and for 1 year thereafter; or serve until the date of the first regular annual meeting and for 2 years thereafter.