When the U.S. Supreme Court said two years ago that hooking a GPS device onto someone’s car to track his movements for a month is unconstitutional, the FBI acknowledged that it had about 3,000 such devices installed around the country. Presumably, the agency would have to go back to trailing these people in unmarked cars. A paper published by two prominent privacy researchers on Thursday in the Yale Law Journal puts some numbers behind the obvious conclusion that doing so would be nearly impossible.

Kevin Bankston, policy director of the New America Foundation’s Open Technology Institute, and Ashkan Soltani, an independent researcher, quantified the per-hour costs of following someone around using various techniques. In order to do the work of those 3,000 GPS devices, the FBI would have to devote every single one of its special agents to surveillance 24 hours a day, and then go out and hire an additional 1,215.

The point of this thought exercise is to solve a question that privacy scholars have been mulling since the Supreme Court said in the 2012 United States v. Jones case that GPS surveillance amounted to a violation of the Fourth Amendment. It’s legal for the police to follow a suspect’s movements in public, but at some point automated surveillance fundamentally changes the equation. A previous Supreme Court ruling has established that putting a beeper on someone’s car, which allows two people to do the work of five people, is legal. You’ve crossed the line once you’ve put a GPS tracker on a car. But where, exactly, is that line?

Bankston and Soltani boil the question down to cost. First, they calculate the per-hour cost of various ways you could track someone’s movement for 28 days. Here are their numbers:

• Assigning a single FBI agent to do it on foot: $50/hr
• Giving that guy a car: $105/hr.
• Having five agents form a “surveillance box” around a suspect: $250/hr
• Giving all those guys cars: $275/hr.
• Giving a single agent a car and attaching a beeper to the suspect’s car: $105/hr
• Using a device called a “stingray” that serves as a simulated cell phone tower, tracking a suspect’s phone: $105/hr
• [Somewhere in here is the line. Ready?]
• Hooking a GPS device into the car’s electrical system: $0.36/hr
• Asking the cell-phone carrier to track his movements: between $0.04/hr and $1.19/hr, depending on the network.

They then come up with an equation that would allow for beeper surveillance, but not GPS surveillance (since that’s what the Supreme Court had ruled.) Here’s their rule of thumb: “If the new tracking technique is an order of magnitude less expensive than the previous technique, the technique violates expectations of privacy and runs afoul of the Fourth Amendment.”

In the future, a judge contemplating whether some new surveillance technology required a warrant could consider this cost equation. The only problem is that GPS tracking seems quaint in the post-Snowden world. Not only does the marginal cost of tracking someone approach zero with mass surveillance, the values are essentially undefined once law enforcement is scanning the population at large, rather than setting a target. Any of the National Security Agency’s surveillance techniques exposed over the last six months would clearly raise the red flag, says Bankston. “Basically, the government has to fish with a pole rather than a net,” he says.

Before it's here, it's on the Bloomberg Terminal. LEARN MORE