On a brilliantly sunny afternoon last October, twenty-eight New Yorkers—some clutching walkers, others in wheelchairs—crammed into a tiny space at the back of Manhattan’s East Side Cafe. While waiters set down blueberry coffee cake, grape jelly, coffee, and orange juice, Maxine Davis, a Medicare account representative from Empire BlueCross BlueShield, raced through the first several pages of the company’s sales booklet. She was promoting MediBlue Plus (HMO), a private plan that Empire offers as an alternative to traditional Medicare. “The maximum amount you pay out of pocket for major medical expenses is sixty-seven hundred dollars. This makes it a…