Cumulative voting is a common method for electing the board of directors of a corporation. The logic is simple: If you allow the shareholders to elect each director separately, a person who holds 51% of the shares can elect every director on the board. With cumulative voting, a minority shareholder can secure at least one seat on the board provided they have enough shares to do so.
Here's a hypothetical: The "Imperial Palace" casino has 100 shares outstanding. Donald Trump owns 51, Kirk Kerkorian owns 30 and Warren Buffett owns 19. There are five seats on the board of directors.
Under plurality voting, the shareholders would vote for each director separately. Trump has 51% of the votes, so he gets to choose each of the five directors.
Under cumulative voting, each shareholder has a number of votes equal to
(shares owned * number of directors)
So Trump has 255 votes, Kerkorian has 150 votes and Buffett has 95 votes. They can allocate these votes however they choose.
Kerkorian starts by voting for himself, using all 150 votes. He is now guaranteed one seat on the board.
Buffett is also guaranteed a seat on the board. This is because if Trump split his vote four ways (to cover all four remaining seats), each would only have 63 or 64 votes. By putting all 95 votes on a single seat, Buffett would squeeze out whichever of Trump's directors had the least votes.
Different jurisdictions have different approaches to cumulative voting. New York, for instance, requires a corporation to affirmatively adopt cumulative voting in its articles of incorporation. Absent this adoption, the corporation has to use plurality voting instead. (If cumulative voting is adopted but later abandoned, minority shareholders have appraisal rights to leave the corporation.) Japan does things differently: shareholders are free to demand cumulative voting unless the system is affirmatively disclaimed in the articles.