Suppose a firm has 10 million shares of common stock out­standing and seven candidates are up for election to three seats on the board of directors. if the firm uses cumulative voting to elect its board, what is the minimum number of votes needed to ensure elec­tion to the board?

7,500,001 votes

Explanation:

total number of votes available is 30 million (= 10 million shares x 3 directors).

If there are seven candidates in the election, then the minimum number of votes needed for a candidate to be elected is one fourth of the votes = 30 million / 4 = 7,500,000 votes.

If any candidate receives at least 7,500,001 (7,500,000 votes + 1 vote) then the remaining 22,499,999 votes will be divided between the other six candidates. Mathematically it is impossible for more than two candidates to get at least 7,500,001 votes each.

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