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Lecture 4 the Empirical Implications of Privacy-aware Choice

Today we’ll be talking about a very different version of privacy than we have seen so far in this class. This notion of privacy is different from differential privacy in two crucial ways. First, we’re going to be looking at individuals rather than databases. If we wanted to apply differentially private algorithms to a database of size one (i.e. for a single individual), we would have to output either pure noise or a constant function, thus losing all accuracy. Differential privacy requires that the output cannot be too sensitive to the input of a single individual, but if the individual is the entire database, then the output of the algorithm cannot be sensitive to the input. For this reason, it doesn’t make sense to talk about differential privacy for a single individual. Second, today we’re not going to add any noise to the observed data. There are many environments “in the wild” where there is no opportunity to add noise. For example, when browsing online, the NSA (presumably) knows our identities and tracks our browsing behavior. When shopping on Amazon, one must be logged in with credit card information and a mailing address. Thus Amazon can identify each shopper individually and records our exact purchases. Similarly at the grocery store checkout, the clerk can physically see each shopper and observes the shopper’s purchases exactly. In these examples, there is no mechanism by which to add noise, because choices are directly observed. A rational individual who knows that she is being watched might change her shopping or browsing behavior to obscure her true preferences. This is exactly the phenomenon we want to explore today: How do people change their behavior when they have concerns for privacy and know that they’re being watched? Can an observer learn about agents’ true preferences by observing choices in this setting? We will see that a rough answer to the latter question is “no.” The observer is not able to reverse engineer the agents’ preferences, without making very strong assumptions on the structural properties of preferences.