Regular readers are familiar with the mosaic theory of the Fourth Amendment, the notion that government monitoring and analysis of many non-searches eventually crosses a threshold and becomes a Fourth Amendment search. The New York Times Bits blog reports that a new law review article claims to have used advances in computer science to solve the mystery of how the mosaic theory applies. According to the Bits blog, the paper has scientifically answered how long location tracking can occur before it violates the Fourth Amendment: About a week. I thought I would explain why the Bits blog misunderstands what the paper says, and why the “one week” claim is not what it seems.

First, here’s what the Bits blog reports:

When does the simple digital tracking of your location and movements — the GPS bleeps from most of our smartphones — start to be truly revealing? When do the data points and inferences that can be drawn from it strongly suggest, say, trips to a psychiatrist, a mosque, an abortion clinic, a strip club or an AIDS treatment center?
The answer, according to a new research paper, is about a week, when the data portrait of a person becomes sufficiently detailed to qualify as an “unreasonable search” and a potential violation of an individual’s Fourth Amendment rights.
The research paper, a collaboration of computer scientists and lawyers, wades into the debate over the legal and policing implications of modern data collection and analysis technology. It explores what in legal circles is called the “mosaic theory” of the Fourth Amendment, which essentially states that when linked and analyzed by software, a much richer picture emerges from combined information than from discrete data points.

It sounds provocative. But if you read the paper, it doesn’t actually make that claim. The article contends that if you have data sets involving tracking information, new machine learning principles can be applied to that data set to reveal trends in that you can’t otherwise easily spot. If the trends reveal a great deal about a person’s life, and you think that revealing a great deal about a person’s life constitutes a Fourth Amendment “search,” then applying machine learning principles to existing location datasets could trigger a Fourth Amendment search at the moment that machine learning can spot the trend that is otherwise not obvious. As stated, the article’s claim is very abstract. We don’t normally have a data set in Fourth Amendment law, and no one yet has developed a clear theory of when a Fourth Amendment mosaic is triggered. Without either, this seems mostly like an interesting thought experiment.

So where did Bits get the idea that science shows that a Fourth Amendment search occurs after “about a week” of monitoring? As far as I can tell, it mostly comes from a press release about the article that includes the following passage:

One objection to [the mosaic theory] theory is very practical: how can police draw the line? Why is three days acceptable while four weeks is not?
“Computer science can provide an answer. The basic idea is very simple: when machine learning techniques — the same sorts of tools that let companies like Amazon and Netflix make accurate recommendations, based on your past history — can make accurate enough predictions, you have a mosaic,” says Steven M. Bellovin, Computer Science (CS) Professor at Columbia Engineering, who co-authored the paper with CS Associate Professor Tony Jebara and PhD candidate Sebastian Zimmeck, both at Columbia Engineering; and Renée M. Hutchins, professor of law at the University of Maryland Carey School of Law.
Their study focuses on how technology — in particular, understanding the data compilation and analysis revealed by machine learning — can provide important Fourth Amendment insights, especially when it comes to long-term surveillance and whether a search warrant is necessary.
“One of the things we discovered,” says Bellovin, who was also chief technology officer of the Federal Trade Commission from 2012 to 2013, “is that the threshold is at most a week, probably less. You can now get predications of startling accuracy with remarkably few data points. The scientific literature shows that the intuitive answer is correct. Most people have reasonably consistent movements during the workweek. As it turns out, weekend movements are pretty regular, too. An observer can get a remarkably full picture of someone’s life in just seven days.”

Based on my reading of the paper, it doesn’t include this claim. I contacted Professor Bellovin to help me understand the evidence he refers to in the press release, and he pointed me to a page in the article that cites two scientific papers. Professor Bellovin thinks that the papers indicate that a Fourth Amendment mosaic search generally exists after seven days of tracking data. But I disagree. Here are the details for you to decide for yourself.

The first paper, Adam Sadilek & John Krumm, Far Out: Predicting Long-Term Human Mobility, Proceedings of the Twenty-Sixth AAAI Conf. on Artificial Intelligence (2012), appears to be the primary source for Bellowin’s claim that the threshold for a mosaic is about a week. For this paper, volunteers in Seattle carried GPS devices with them on their persons (about 300 people) and in commercial vehicles (about 400 people). The authors wanted to know the consistency of how people travel over time. The basic finding was pretty much what common sense tells you: Most people have a pretty consistent travel schedules over the course of a week. If you think about it, most people are at home at night and at school or work during week school and work hours. So if a person is known to be in a particular place at a particular time and date one week, there’s a decent chance that she’ll be in the same place at the same day and time in a future week.

The second paper, Song et. al. Limits of Predictability in Human Mobility, 327 Science 1018 (Feb 2010), is somewhat similar. In this paper, the authors obtained cell-site records of 50,000 anonymized individuals. It found that the cell towers that individual phones connect to over the course of a day follow relatively consistent patterns for that particular phone. Again, this seems pretty intuitive. Most people are at home at night and at school or work during the day. When a person is at home, her phone will probably connect to the tower near home; when the person is at school or work, her phone will probably connect to the tower near school or work. Because most people are at home and night and at school or work when they have to be, and they take the same path to school or work and back each day, the patterns of the cell towers that their phones connect to would be expected to match those patterns.

Bellovin concludes that these papers indicate that an unreasonable search probably occurs by around seven days. The thinking seems to go something like this: One day’s worth of location tracking tells you a lot about a person by suggesting where a person lives and works and the like. And by the time you get to a week of tracking, you can make predictions of how the person spends weekends, too. So by a week of tracking, the government has enough information on someone to constitute a mosaic.

There are big problems with this argument, though. The real work is being done by the claim that having a basis for predicting where a person will be over time to some degree of specificity is enough to create a Fourth Amendment “mosaic” about them. That’s a legal argument, not a scientific conclusion. “Science” doesn’t answer it. And as a legal argument, it’s a very novel claim. I don’t recall proponents of the mosaic theory advocating this as a standard. It seems pretty different from the standards of the mosaic hinted at in the Maynard decision or the Jones concurrences. So while it’s answering a question, it’s not clear that it’s the Fourth Amendment question that the mosaic theory asks.