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Information Design for Differential Privacy

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  • Ian M. Schmutte
  • Nathan Yoder

Abstract

Firms and statistical agencies must protect the privacy of the individuals whose data they collect, analyze, and publish. Increasingly, these organizations do so by using publication mechanisms that satisfy differential privacy. We consider the problem of choosing such a mechanism so as to maximize the value of its output to end users. We show that this is a constrained information design problem, and characterize its solution. When the underlying database is drawn from a symmetric distribution -- for instance, if individuals' data are i.i.d. -- we show that the problem's dimensionality can be reduced, and that its solution belongs to a simpler class of mechanisms. When, in addition, data users have supermodular payoffs, we show that the simple geometric mechanism is always optimal by using a novel comparative static that ranks information structures according to their usefulness in supermodular decision problems.

Suggested Citation

  • Ian M. Schmutte & Nathan Yoder, 2022. "Information Design for Differential Privacy," Papers 2202.05452, arXiv.org, revised Dec 2022.
    • Handle: RePEc:arx:papers:2202.05452
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    References listed on IDEAS

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    1. Emir Kamenica, 2019. "Bayesian Persuasion and Information Design," Annual Review of Economics, Annual Reviews, vol. 11(1), pages 249-272, August.
    2. Charles I. Jones & Christopher Tonetti, 2020. "Nonrivalry and the Economics of Data," American Economic Review, American Economic Association, vol. 110(9), pages 2819-2858, September.
    3. Margaret Meyer & Bruno Strulovici, 2013. "The Supermodular Stochastic Ordering," Discussion Papers 1563, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    4. John M. Abowd & Ian M. Schmutte & William N. Sexton & Lars Vilhuber, 2019. "Why the Economics Profession Must Actively Participate in the Privacy Protection Debate," AEA Papers and Proceedings, American Economic Association, vol. 109, pages 397-402, May.
    5. Le Treust, Maël & Tomala, Tristan, 2019. "Persuasion with limited communication capacity," Journal of Economic Theory, Elsevier, vol. 184(C).
    6. John K.-H. Quah & Bruno Strulovici, 2009. "Comparative Statics, Informativeness, and the Interval Dominance Order," Econometrica, Econometric Society, vol. 77(6), pages 1949-1992, November.
    7. Raj Chetty & John N. Friedman, 2019. "A Practical Method to Reduce Privacy Loss When Disclosing Statistics Based on Small Samples," AEA Papers and Proceedings, American Economic Association, vol. 109, pages 414-420, May.
    8. Briana Chang & Martin Szydlowski, 2020. "The Market for Conflicted Advice," Journal of Finance, American Finance Association, vol. 75(2), pages 867-903, April.
    9. Emir Kamenica & Matthew Gentzkow, 2011. "Bayesian Persuasion," American Economic Review, American Economic Association, vol. 101(6), pages 2590-2615, October.
    10. Athey, Susan & Levin, Jonathan, 2018. "The value of information in monotone decision problems," Research in Economics, Elsevier, vol. 72(1), pages 101-116.
    11. John M. Abowd & Ian M. Schmutte, 2019. "An Economic Analysis of Privacy Protection and Statistical Accuracy as Social Choices," American Economic Review, American Economic Association, vol. 109(1), pages 171-202, January.
    12. Nicola Persico, 1996. "Information Acquisition in Affiliated Decision Problems," Discussion Papers 1149, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    13. Imanol Arrieta-Ibarra & Leonard Goff & Diego Jiménez-Hernández & Jaron Lanier & E. Glen Weyl, 2018. "Should We Treat Data as Labor? Moving beyond "Free"," AEA Papers and Proceedings, American Economic Association, vol. 108, pages 38-42, May.
    14. Jeffrey C. Ely, 2017. "Beeps," American Economic Review, American Economic Association, vol. 107(1), pages 31-53, January.
    15. Paul R. Milgrom, 1981. "Good News and Bad News: Representation Theorems and Applications," Bell Journal of Economics, The RAND Corporation, vol. 12(2), pages 380-391, Autumn.
    16. Michael Ostrovsky & Michael Schwarz, 2010. "Information Disclosure and Unraveling in Matching Markets," American Economic Journal: Microeconomics, American Economic Association, vol. 2(2), pages 34-63, May.
    17. Marina Halac & Elliot Lipnowski & Daniel Rappoport, 2021. "Rank Uncertainty in Organizations," American Economic Review, American Economic Association, vol. 111(3), pages 757-786, March.
    18. Larry G. Epstein & Stephen M. Tanny, 1980. "Increasing Generalized Correlation: A Definition and Some Economic Consequences," Canadian Journal of Economics, Canadian Economics Association, vol. 13(1), pages 16-34, February.
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    Cited by:

    1. Kai Hao Yang & Philipp Strack, 2023. "Privacy Preserving Signals," Cowles Foundation Discussion Papers 2379, Cowles Foundation for Research in Economics, Yale University.

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