## Abstract

The notion of a universally utility-maximizing privacy mechanism was introduced by Ghosh, Roughgarden, and Sundararajan [Proceedings of STOC, 2009]. These are mechanisms that guarantee optimal utility to a large class of information consumers, simultaneously, while preserving privacy. They demonstrated, quite surprisingly, a case where such a universally utility-maximizing privacy mechanism exists, when the information consumers are Bayesian. This result was later extended by Gupte and Sundararajan [Proceedings of 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). We show that such universally optimal mechanisms do not exist for some natural extensions of count 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 by its privacy constraint graph whose edges correspond to values resulting by applying the query function to neighboring databases.

Original language | English |
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Pages (from-to) | 1513-1540 |

Number of pages | 28 |

Journal | SIAM Journal on Computing |

Volume | 43 |

Issue number | 5 |

DOIs | |

State | Published - 1 Jan 2014 |

## Keywords

- Differential privacy
- Universal optimality

## ASJC Scopus subject areas

- General Computer Science
- General Mathematics