There is an election being held to fill two seats on the board of directors of a firm in which you hold stock. There are a total of 420 shares outstanding. If the election is conducted under cumulative voting and you own 120 shares, how many more shares must you buy to be assured of earning a seat on the board?

Question

Quizplus · Accepted Answer

Under cumulative voting, each shareholder may cast all their votes for a single candidate. To guarantee a win for one seat in a two-seat election, you need over 1/3 of the total votes because the total votes cast will be 420 shares * 2 seats = 840 votes. To control over 1/3 of the votes, you need more than 840 / 3 = 280 votes. Owning 120 shares, you need 281 votes to ensure control - 120 = 161 more votes. Since each share equals one vote, you need to buy 161 more shares. However, the options provided do not match this calculation, indicating a mistake in my initial explanation. Correcting this: to ensure a win, you actually need just over 1/3 of the total shares, not votes. With 420 shares outstanding, 1/3 is 140. To ensure a win, you need 141 shares, but since you already have 120, you need 21 more shares to have a total of 141, ensuring control over more than 1/3 of the shares and a seat on the board.

There Is an Election Being Held to Fill Two Seats