“Among leading A.I. teams, many can likely replicate others’ software in, at most, one to two years,” notes the technologist Andrew Ng. “But it is exceedingly difficult to get access to someone else’s data. Thus data, rather than software, is the defensible barrier for many businesses.”

We may think we get a fair deal, offering our data as the price of sharing puppy pictures. By other metrics, we are being victimized: In the largest technology companies, the share of income going to labor is only about 5 to 15 percent, Mr. Posner and Mr. Weyl write. That’s way below Walmart’s 80 percent. Consumer data amounts to work they get free.

“If these A.I.-driven companies represent the future of broader parts of the economy,” they argue, “without something basic changing in their business model, we may be headed for a world where labor’s share falls dramatically from its current roughly 70 percent to something closer to 20 to 30 percent.”

As Mr. Lanier, Mr. Posner and Mr. Weyl point out, it is ironic that humans are providing free data to train the artificial-intelligence systems to replace workers across the economy. Commentators from both left and right fret over how ordinary people will put food on the table once robots take all the jobs. Perhaps a universal basic income, funded by taxes, is the answer?

How about paying people for the data they produced to train the robots? If A.I. accounted for 10 percent of the economy and the big-data companies paid two-thirds of their income for data — the same as labor’s share of income across the economy — the share of income going to “workers” would rise drastically. By Mr. Weyl and Mr. Posner’s reckoning, the median household of four would gain $20,000 a year.

A critical consideration is that if people were paid for their data, its quality and value would increase. Facebook could directly ask users to tag the puppy pictures to train the machines. It could ask translators to upload their translations. Facebook and Google could demand quality information if the value of the transaction were more transparent. Unwilling to enter in a direct quid pro quo with their users, the data titans must make do with whatever their users submit.

The transition would not be painless. We would need to figure out systems to put value on data. Your puppy pictures might turn out to be worthless, but that college translation from Serbo-Croatian could be valuable. Barred from free data, YouTube and Facebook might charge a user fee for their service — like Netflix. Alternatively, they might make their money from training A.I. systems and pay some royalty stream to the many people whose data helped train them.