Can Swapping be Differentially Private? A Refreshment Stirred, not Shaken

We thank Daniel Susser for his helpful and stimulating feedback on earlier drafts of this work, and Priyanka Nanayakkara and Océane Marescal for their valuable suggestions and proofreading of later drafts. We are grateful to the participants of the National Bureau of Economic Research's conference "Data Privacy Protection and the Conduct of Applied Research: Methods, Approaches and Their Consequences" (May 4-5, 2023); the 36th New England Statistical Symposium's invited session "A Private Refreshment on Statistical Principles and Senses" (June 6, 2023); the 2023 Joint Statistical Meetings session "Methodological Approaches to Privacy Concerns Across Multiple Domains" (August 10, 2023); the CA Census retreat at the Boston University Center for Computing and Data Science (September 26, 2023); and the Statistics Canada Methodology Seminar (October 31, 2023) for their thoughtful comments and questions. We appreciate enormously the detailed feedback provided by Daniel Kifer, John Abowd, Philip Leclerc, Ryan Cummings, Rolando Rodriguez, Robert Ashmead, Sallie Keller and Michael Hawes at the US Census Bureau, which greatly improved and corrected all three parts of this trio of papers. All remaining errors are purely our own. JB gratefully acknowledges partial financial support from the Australian-American Fulbright Commission and the Kinghorn Foundation; RG and XLM acknowledge partial financial support from the NSF; and XLM acknowledges partial financial support from Harvard University's Office of the Vice Provost for Research.