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DOI: 10.4230/LIPIcs.FORC.2025.8

Differential Privacy Under Multiple Selections

Authors: Ashish Goel, Zhihao Jiang, Aleksandra Korolova, Kamesh Munagala, and Sahasrajit Sarmasarkar

Published in: LIPIcs, Volume 329, 6th Symposium on Foundations of Responsible Computing (FORC 2025)

Abstract

We consider the setting where a user with sensitive features wishes to obtain a recommendation from a server in a differentially private fashion. We propose a "multi-selection" architecture where the server can send back multiple recommendations and the user chooses one from these that matches best with their private features. When the user feature is one-dimensional - on an infinite line - and the accuracy measure is defined w.r.t some increasing function 𝔥(.) of the distance on the line, we precisely characterize the optimal mechanism that satisfies differential privacy. The specification of the optimal mechanism includes both the distribution of the noise that the user adds to its private value, and the algorithm used by the server to determine the set of results to send back as a response. We show that Laplace is an optimal noise distribution in this setting. Furthermore, we show that this optimal mechanism results in an error that is inversely proportional to the number of results returned when the function 𝔥(.) is the identity function.

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Ashish Goel, Zhihao Jiang, Aleksandra Korolova, Kamesh Munagala, and Sahasrajit Sarmasarkar. Differential Privacy Under Multiple Selections. In 6th Symposium on Foundations of Responsible Computing (FORC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 329, pp. 8:1-8:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{goel_et_al:LIPIcs.FORC.2025.8,
  author =	{Goel, Ashish and Jiang, Zhihao and Korolova, Aleksandra and Munagala, Kamesh and Sarmasarkar, Sahasrajit},
  title =	{{Differential Privacy Under Multiple Selections}},
  booktitle =	{6th Symposium on Foundations of Responsible Computing (FORC 2025)},
  pages =	{8:1--8:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-367-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{329},
  editor =	{Bun, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2025.8},
  URN =		{urn:nbn:de:0030-drops-231353},
  doi =		{10.4230/LIPIcs.FORC.2025.8},
  annote =	{Keywords: Differential Privacy, Mechanism Design and Multi-Selection}
}

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Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2023.70

Low Sample Complexity Participatory Budgeting

Authors: Mohak Goyal, Sukolsak Sakshuwong, Sahasrajit Sarmasarkar, and Ashish Goel

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

Abstract

We study low sample complexity mechanisms in participatory budgeting (PB), where each voter votes for a preferred allocation of funds to various projects, subject to project costs and total spending constraints. We analyse the distortion that PB mechanisms introduce relative to the minimum-social-cost outcome in expectation. The Random Dictator mechanism for this problem obtains a distortion of 2. In a special case where every voter votes for exactly one project, [Fain et al., 2017] obtain a distortion of 4/3. We show that when PB outcomes are determined as any convex combination of the votes of two voters, the distortion is 2. When three uniformly randomly sampled votes are used, we give a PB mechanism that obtains a distortion of at most 1.66, thus breaking the barrier of 2 with the smallest possible sample complexity. We give a randomized Nash bargaining scheme where two uniformly randomly chosen voters bargain with the disagreement point as the vote of a voter chosen uniformly at random. This mechanism has a distortion of at most 1.66. We provide a lower bound of 1.38 for the distortion of this scheme. Further, we show that PB mechanisms that output a median of the votes of three voters chosen uniformly at random, have a distortion of at most 1.80.

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Mohak Goyal, Sukolsak Sakshuwong, Sahasrajit Sarmasarkar, and Ashish Goel. Low Sample Complexity Participatory Budgeting. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 70:1-70:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{goyal_et_al:LIPIcs.ICALP.2023.70,
  author =	{Goyal, Mohak and Sakshuwong, Sukolsak and Sarmasarkar, Sahasrajit and Goel, Ashish},
  title =	{{Low Sample Complexity Participatory Budgeting}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{70:1--70:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.70},
  URN =		{urn:nbn:de:0030-drops-181223},
  doi =		{10.4230/LIPIcs.ICALP.2023.70},
  annote =	{Keywords: Social Choice, Participatory budgeting, Nash bargaining}
}

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Differential Privacy Under Multiple Selections

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Low Sample Complexity Participatory Budgeting

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