Impossibility of differentially private universally optimal mechanisms

Hai Brenner, Kobbi Nissim

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

46 Scopus citations


The notion of a universally utility-maximizing privacy mechanism was recently introduced by Ghosh, Roughgarden, and Sundararajan [STOC 2009]. These are mechanisms that guarantee optimal utility to a large class of information consumers, simultaneously, while preserving Differential Privacy [Dwork, McSherry, Nissim, and Smith, TCC 2006]. Ghosh, Roughgarden and Sundararajan have demonstrated, quite surprisingly, a case where such a universally-optimal differentially-private mechanisms exists, when the information consumers are Bayesian. This result was recently extended by Gupte and Sundararajan [PODS 2010] to risk-averse consumers. Both positive results deal with mechanisms (approximately) computing a single count query (i.e., the number of individuals satisfying a specific property in a given population), and the starting point of our work is a trial at extending these results to similar settings, such as sum queries with non-binary individual values, histograms, and two (or more) count queries. We show, however, that universally-optimal mechanisms do not exist for all these queries, both for Bayesian and risk-averse consumers. For the Bayesian case, we go further, and give a characterization of those functions that admit universally-optimal mechanisms, showing that a universally-optimal mechanism exists, essentially, only for a (single) count query. At the heart of our proof is a representation of a query function f by its privacy constraint graph G f whose edges correspond to values resulting by applying f to neighboring databases.

Original languageEnglish
Title of host publicationProceedings - 2010 IEEE 51st Annual Symposium on Foundations of Computer Science, FOCS 2010
PublisherInstitute of Electrical and Electronics Engineers
Number of pages10
ISBN (Print)9780769542447
StatePublished - 1 Jan 2010
Event2010 IEEE 51st Annual Symposium on Foundations of Computer Science, FOCS 2010 - Las Vegas, United States
Duration: 23 Oct 201026 Oct 2010

Publication series

NameProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
ISSN (Print)0272-5428


Conference2010 IEEE 51st Annual Symposium on Foundations of Computer Science, FOCS 2010
Country/TerritoryUnited States
CityLas Vegas


  • Differential privacy
  • Geometric mechanism
  • Universally optimal mechanisms
  • Utility

ASJC Scopus subject areas

  • Computer Science (all)

Cite this