Hoffman, who founded LinkedIn, has a premise about how the economic world will work from now on. Illustration by Stanley Chow

Early on a Monday evening in June, Reid Hoffman, the founder and executive chairman of the business-oriented networking site LinkedIn, met Mark Pincus, the founder and chief executive of the gaming site Zynga, for dinner at a casual restaurant in Portola Valley, California, a wealthy residential town at the western edge of Silicon Valley. Breakfasts and dinners are a big part of Hoffman’s life. He recently published two books on how to be successful in business, and is finishing a third, whose working title is “Blitzscaling.” His business is based on the idea of managing your career through relentless networking, which is something he enjoys.

If someone told you that Hoffman was the equipment manager for a Pearl Jam tour, it wouldn’t seem like a casting error. He is a big, broad-faced man with tousled brown hair, who typically dresses for work in black shorts, a black T-shirt, running shoes, and white socks. He befriended Pincus about twenty years ago, when the two met in the Bay Area to discuss business ideas, and discovered that they both believed that social media would be the next big thing in Silicon Valley. At dinner, Hoffman was wearing two watches, one on each wrist—an Apple Watch and a competing product—so he could see which one he liked better. He bustled in a few minutes late, sat down, and pulled out a small notebook filled with an indecipherable scrawl.

“Joss Whedon,” Hoffman said, referring to the film and television director who specializes in material about vampires and comic-book characters. “Is he somebody you think is cool and fun? No? I’m interviewing him on Wednesday.”

“I have a recruiting dinner,” Pincus said. “Actually a re-recruiting dinner.” He is a forty-nine-year-old triathlete, small and lithe, with a long flop of hair. He was wearing a T-shirt, jeans, and sneakers.

Hoffman shrugged. “Anything top of mind? ’Cause I have a list.” Hoffman tries to begin all meals with a ritual in which both parties write down a list of the topics they want to discuss.

“I made a connection between the things we were talking about with the President and the Summer of Love,” Pincus said.

During President Obama’s reëlection campaign, in 2012, Hoffman and Pincus each gave a million dollars to Priorities USA, the Democratic Super PAC. Since then, they have had the opportunity to spend time with Obama. In a private forty-five-minute meeting in the Oval Office in 2012, Pincus gave the President a PowerPoint presentation on what he calls “the product-management approach to government.” Obama telephones him now and then, sometimes at home, and Pincus and his wife have been Obama’s dinner guests.

In June, Hoffman helped organize the guest list for a dinner party for Obama in San Francisco, and he has had conversations with Obama at several meetings and dinners at the White House. One was for a small group that included Toni Morrison and the actress Eva Longoria, convened to give Obama advice about his post-Presidency. Hoffman and his wife, Michelle Yee, also attended the state dinner in late September for Xi Jinping, the President of China.

LinkedIn has provided the White House with some of the trove of data it has collected about its users’ activities in the job market; the data have been used in the annual Economic Report of the President. Earlier this year, a former LinkedIn executive, DJ Patil, was named to the new position of chief data scientist in the White House. In July, Hoffman organized a meeting for people involved with Obama’s new foundation on how to better harness the power of social networks. His list for dinner with Pincus included the question of what to discuss at that meeting.

The close relationship between Hoffman and the White House isn’t just about his being a major political donor. He and others like him have something more powerful than money to offer: a way for officials to connect with the largest possible audiences. In the nineteenth century, the bosses of political machines served this role; in the twentieth, it was media barons, especially in broadcasting and newspapers; in the twenty-first, it is people who have created vast online social networks.

This year’s Super Bowl attracted the biggest audience in the history of American network television—a hundred and fourteen million people. That represents an annual peak in the life of a declining medium. The three traditional evening broadcast news programs together draw twenty-two million viewers. Every day, a hundred and sixty-four million people in the U.S. and Canada, and up to a billion people worldwide, are active on Facebook.

Obama has said that he wants to encourage civic engagement after he leaves the White House. Silicon Valley can provide powerful tools to accomplish that. The same calculus draws people from Hollywood, such as Joss Whedon, on regular pilgrimages north to meet with Hoffman and others. And it’s why, when the launch of the HealthCare.gov Web site failed spectacularly in the fall of 2013, the White House’s chief technology officer (a friend of Hoffman’s) hired a team of Silicon Valley executives to help fix it.

In politics as in the rest of life, relationships move in two directions. Along with whatever help Obama gets in Silicon Valley, he will absorb some of its view of the world. In that view, humanity is a kind of Prometheus bound by a constricting web of old institutional arrangements that the Internet must clear away. Reid Hoffman and his friends have got very skillful at politics, nationally and globally, and their ideas have a good chance of being implemented.

“Why don’t we start with the Summer of Love?” Hoffman said.

Pincus shook his head. “No, let’s start with your list.”

“This jousting—I hope you’re not doing it on my account.” Facebook

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Hoffman ticked off a few items: An upper-level undergraduate computer-science class he’s teaching at Stanford called “Technology-Enabled Blitzscaling.” Twitch, an online video platform for gamers. His recent meetings with George Osborne, the Chanceller of the Exchequer of the United Kingdom; Ban Ki-moon, the Secretary-General of the United Nations; the Duke of York; and the minister of cabinet affairs of the United Arab Emirates. How Hoffman and Pincus manage their wealth. (Hoffman is worth between three and four billion dollars, which puts him between twentieth and thirtieth place on the list of Silicon Valley’s richest people.)

“Oh, and one more,” he said. “Are you stacking A.I. at all?”

“I got that book ‘Superintelligence,’ ” Pincus said.

“I’ve actually decided it’s worth going deep on,” Hoffman said.

They finished the items on Hoffman’s list. “So let’s go to the President,” Hoffman said. “Start with my view or your view?”

“He’s coming back to his strength, being an orator to the people,” Pincus said. “When I had my one-on-one with him, I said, ‘Where’s Preacher Obama? And Obama the fighter? Scrappy with Congress, in the fray.’ When he’s Preacher Obama, he goes back to that J.F.K. place. My favorite moment was at the end, when he said, ‘Unless we solve governance, you’re not going to have the impact you want to have.’ ”

They talked for a while about ways the political system might be fixed through online activism. Last year, Hoffman contributed a million dollars to Mayday, the crowdfunded Super Pac founded by Lawrence Lessig, the Harvard law professor who is now running for President. Mayday is designed to end all Super PACs, removing big money from politics.