Gonczarowski, YannaiVadhan, SalilTang, Jason2026-03-0420252025-06-242025Tang, Jason. 2025. The Best of Three Worlds? Privacy, Welfare, and Fairness for Facility Location Mechanism Design. Bachelors Thesis, Harvard University Engineering and Applied Sciences.31932072https://dash.harvard.edu/handle/1/42731098The facility location problem in economics examines where a public facility should be placed to maximize the total welfare of its prospective users. While this objective, termed social welfare, is the primary focus of traditional literature on facility location, other factors must also be considered in real-world implementations. One such desideratum is privacy: the welfare-maximizing location for the facility may be determined by highly personalized data about the population (e.g., where people live and which individuals are likely to utilize the facility), so it is important to ensure that the process (or "mechanism") of selecting the facility location does not inadvertently leak this sensitive information to the public. However, to protect against such privacy risks, a facility location mechanism must reduce its reliance on individualized data. Consequently, the resulting privacy-preserving output will yield lower social welfare than the optimal spot for the facility, producing a welfare loss that can be viewed as the "cost of privacy." This illustrates a tradeoff between social welfare and privacy that existing research already covers. Yet, the imposition of privacy also induces a third consideration that has not been similarly studied: fairness in how the "cost of privacy" is distributed across individuals. For instance, suppose we can make a mechanism private while only incurring a small loss in social welfare, but this welfare loss is entirely borne by a single individual. Even though this implementation minimizes the privacy-social welfare tradeoff, it would still be undesirable as it disproportionately harms select members of the population. In this thesis, we therefore consider three objectives simultaneously and ask: What is the tradeoff between privacy, social welfare, and fairness when designing mechanisms for facility location? We quantify privacy through the framework of differential privacy, utilize a standard measure of social welfare, and propose a novel measure of fairness. Under this setup, we first derive an impossibility result that privacy and fairness cannot be simultaneously guaranteed over all possible datasets that could represent the locations of individuals in a population. We then offer a relaxation of the original problem that only seeks fairness and social welfare over smaller, more "realistic-looking" families of datasets. For this relaxation, we construct a private mechanism M and prove high probability upper bounds on its loss with respect to fairness and social welfare. At the same time, we derive information-theoretic lower bounds on the amount of fairness and social welfare loss that any differentially private mechanism must incur. A comparison of these bounds shows that in addition to being differentially private, our mechanism M is simultaneously optimal (or, for a harder family of datasets, near-optimal up to small factors) on fairness and social welfare. This suggests that while there is a tradeoff between privacy and each of social welfare and fairness, there is no additional tradeoff when we consider all three objectives simultaneously, provided that the population data is sufficiently "natural."application/pdfenDifferential PrivacyFacility LocationFairnessComputer scienceEconomicsMathematicsThesis or Dissertation2026-03-04