Low Sample Complexity Participatory Budgeting

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

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Mohak Goyal
  • Stanford University, CA, USA
Sukolsak Sakshuwong
  • Stanford University, CA, USA
Sahasrajit Sarmasarkar
  • Stanford University, CA, USA
Ashish Goel
  • Stanford University, CA, USA


We would like to thank Lodewijk Gelauff, (Stanford University), Geoff Ramseyer(Stanford University) and Kamesh Munagala(Duke University) for valuable insights and discussions on the paper and the introduction.

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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)


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.

Subject Classification

ACM Subject Classification
  • Applied computing
  • Social Choice
  • Participatory budgeting
  • Nash bargaining


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