EBay’s billionaire founder and proponent of good works was addressing a roomful of White House Fellows in a closed-door question-and-answer session last month, hours before President Obama’s State of the Union address, when a query stumped him: What do you hope to accomplish the rest of your life?

Omidyar, 44, looked down, contemplatively, then fixed his eyes on the questioner. “We live a comfortable life, but relationships are what make a life rich,” he said. Omidyar, a member of the president’s Commission on White House Fellowships, touched on a mix of causes that include media democracy, education and the difference between charity (“a quick solution”) and philanthropy (“systemic changes to long-term problems”).