In cumulative voting for directors, which formula determines the minimum shares to win one seat if there are s seats?

• A. Total shares divided by number of seats
• B. 50% of total shares
• C. One vote per share
• D. (100 ÷ (seats + 1)) × total shares + 1

Answer: (D)

In cumulative voting, you can concentrate all your votes on a single candidate. To guarantee winning one seat when there are s seats, you must command more than the share of votes that could be spread across the other s candidates. The minimum number of shares needed is the total voting power divided by (s + 1), with any fraction rounded up, and then you add one more vote to guarantee the win. This is exactly the form shown: divide total shares by (seats + 1), then add one.

For example, with 100 total shares and four seats, you’d need floor(100/5) + 1 = 20 + 1 = 21 shares to guarantee a seat. This reflects why the threshold depends on the number of seats: as more seats are available, a smaller fraction is enough to win a seat, but you still need one more vote beyond that fractional threshold.

Why other ideas don’t fit: dividing by the number of seats would imply an equal split without accounting for concentration of votes, and requiring 50% is too strong a condition when multiple seats are up for grabs. One vote per share describes simple plurality voting, not cumulative voting where votes can be pooled.