Hedge-fund titan Bill Ackman has vowed to bring down Herbalife, the 33-year-old nutritional-supplement company, which he views as a pyramid scheme. With his massive shorting of Herbalife stock, the price plummeted, prompting two fellow billionaires—Ackman’s former friend Dan Loeb and activist investor Carl Icahn—to take the opposing bet on Herbalife. As the public brawl rivets Wall Street, William D. Cohan learns why, this time, it’s personal