On Fair and Efficient Allocations of Indivisible Public Goods

Authors Jugal Garg, Pooja Kulkarni, Aniket Murhekar



PDF
Thumbnail PDF

File

LIPIcs.FSTTCS.2021.22.pdf
  • Filesize: 0.71 MB
  • 19 pages

Document Identifiers

Author Details

Jugal Garg
  • University of Illinois, Urbana-Champaign, IL, USA
Pooja Kulkarni
  • University of Illinois, Urbana-Champaign, IL, USA
Aniket Murhekar
  • University of Illinois, Urbana-Champaign, IL, USA

Cite AsGet BibTex

Jugal Garg, Pooja Kulkarni, and Aniket Murhekar. On Fair and Efficient Allocations of Indivisible Public Goods. In 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 213, pp. 22:1-22:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.FSTTCS.2021.22

Abstract

We study fair allocation of indivisible public goods subject to cardinality (budget) constraints. In this model, we have n agents and m available public goods, and we want to select k ≤ m goods in a fair and efficient manner. We first establish fundamental connections between the models of private goods, public goods, and public decision making by presenting polynomial-time reductions for the popular solution concepts of maximum Nash welfare (MNW) and leximin. These mechanisms are known to provide remarkable fairness and efficiency guarantees in private goods and public decision making settings. We show that they retain these desirable properties even in the public goods case. We prove that MNW allocations provide fairness guarantees of Proportionality up to one good (Prop1), 1/n approximation to Round Robin Share (RRS), and the efficiency guarantee of Pareto Optimality (PO). Further, we show that the problems of finding MNW or leximin-optimal allocations are NP-hard, even in the case of constantly many agents, or binary valuations. This is in sharp contrast to the private goods setting that admits polynomial-time algorithms under binary valuations. We also design pseudo-polynomial time algorithms for computing an exact MNW or leximin-optimal allocation for the cases of (i) constantly many agents, and (ii) constantly many goods with additive valuations. We also present an O(n)-factor approximation algorithm for MNW which also satisfies RRS, Prop1, and 1/2-Prop.

Subject Classification

ACM Subject Classification
  • Theory of computation → Mathematical optimization
Keywords
  • Public goods
  • Nash welfare
  • Leximin
  • Proportionality

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads

References

  1. S Airiau, H Aziz, I Caragiannis, J Kruger, and J Lang. Positional social decision schemes: Fair and efficient portioning. In Proceedings of the 7th International Workshop on Computational Social Choice (COMSOC), 2018. Google Scholar
  2. Haris Aziz, Markus Brill, Vincent Conitzer, Edith Elkind, Rupert Freeman, and Toby Walsh. Justified representation in approval-based committee voting. In Proceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligence, pages 784-790, 2015. Google Scholar
  3. Haris Aziz, Barton E. Lee, and Nimrod Talmon. Proportionally representative participatory budgeting: Axioms and algorithms. In Proceedings of the 17th International Conference on Autonomous Agents and MultiAgent Systems (AAMAS), pages 23-31, 2018. Google Scholar
  4. Haris Aziz and Nisarg Shah. Participatory budgeting: Models and approaches. arXiv preprint, 2020. URL: http://arxiv.org/abs/2003.00606.
  5. Ashwinkumar Badanidiyuru, Shahar Dobzinski, and Sigal Oren. Optimization with demand oracles. Algorithmica, 81(6):2244-2269, 2019. Google Scholar
  6. Siddharth Barman and Sanath Krishnamurthy. On the proximity of markets with integral equilibria. In Proceedings of the 33rd AAAI Conference on Artificial Intelligence, pages 1748-1755, 2019. Google Scholar
  7. Siddharth Barman, Sanath Kumar Krishnamurthy, and Rohit Vaish. Finding fair and efficient allocations. In Proceedings of the 2018 ACM Conference on Economics and Computation (EC), pages 557-574, 2018. Google Scholar
  8. Siddharth Barman, Sanath Kumar Krishnamurthy, and Rohit Vaish. Greedy algorithms for maximizing Nash social welfare. In Proceedings of the 17th International Conference on Autonomous Agents and MultiAgent Systems (AAMAS), pages 7-13, 2018. Google Scholar
  9. Ivona Bezáková and Varsha Dani. Allocating indivisible goods. SIGecom Exch., 5(3):11-18, April 2005. Google Scholar
  10. S.J. Brams and A.D. Taylor. Fair Division: From Cake-Cutting to Dispute Resolution. Cambridge University Press, 1996. Google Scholar
  11. Ioannis Caragiannis, David Kurokawa, Hervé Moulin, Ariel D. Procaccia, Nisarg Shah, and Junxing Wang. The unreasonable fairness of maximum Nash welfare. In Proceedings of the 2016 ACM Conference on Economics and Computation (EC), pages 305-322, 2016. Google Scholar
  12. Bhaskar Ray Chaudhury, Yun Kuen Cheung, Jugal Garg, Naveen Garg, Martin Hoefer, and Kurt Mehlhorn. On fair division for indivisible items. In 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS), pages 25:1-25:17, 2018. Google Scholar
  13. Yu Cheng, Zhihao Jiang, Kamesh Munagala, and Kangning Wang. Group fairness in committee selection. In Proceedings of the 2019 ACM Conference on Economics and Computation, pages 263-279, 2019. Google Scholar
  14. Richard Cole and Vasilis Gkatzelis. Approximating the Nash social welfare with indivisible items. In Proceedings of the forty-seventh annual ACM symposium on Theory of computing (STOC), pages 371-380, 2015. Google Scholar
  15. Vincent Conitzer, Rupert Freeman, and Nisarg Shah. Fair public decision making. In Proceedings of the 2017 ACM Conference on Economics and Computation (EC), pages 629-646, 2017. Google Scholar
  16. Andreas Darmann and Joachim Schauer. Maximizing Nash product social welfare in allocating indivisible goods. SSRN Electronic Journal, 247, January 2014. Google Scholar
  17. Brandon Fain, Ashish Goel, and Kamesh Munagala. The core of the participatory budgeting problem. In Web and Internet Economics (WINE), pages 384-399, 2016. Google Scholar
  18. Brandon Fain, Kamesh Munagala, and Nisarg Shah. Fair allocation of indivisible public goods. In Proceedings of the 2018 ACM Conference on Economics and Computation (EC), pages 575-592, 2018. Google Scholar
  19. Till Fluschnik, Piotr Skowron, Mervin Triphaus, and Kai Wilker. Fair knapsack. In Proceedings of the AAAI Conference on Artificial Intelligence (AAAI), pages 1941-1948, 2019. Google Scholar
  20. Rupert Freeman, Sujoy Sikdar, Rohit Vaish, and Lirong Xia. Equitable allocations of indivisible goods. In Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence (IJCAI), pages 280-286, 2019. Google Scholar
  21. Jugal Garg, Martin Hoefer, and Kurt Mehlhorn. Satiation in Fisher markets and approximation of Nash social welfare. CoRR, abs/1707.04428, 2017. URL: http://arxiv.org/abs/1707.04428.
  22. Jugal Garg, Edin Husic, and László A. Végh. Approximating Nash social welfare under Rado valuations. In STOC '21: 53rd Annual ACM SIGACT Symposium on Theory of Computing, Virtual Event, Italy, June 21-25, 2021, pages 1412-1425, 2021. Google Scholar
  23. Jugal Garg, Pooja Kulkarni, and Aniket Murhekar. On fair and efficient allocations of indivisible public goods. CoRR, abs/2107.09871, 2021. URL: http://arxiv.org/abs/2107.09871.
  24. M. S. Klamkin and D. J. Newman. Extensions of the Weierstrass product inequalities. Mathematics Magazine, 43(3):137-141, 1970. URL: http://www.jstor.org/stable/2688388.
  25. Mayuresh Kunjir, Brandon Fain, Kamesh Munagala, and Shivnath Babu. ROBUS: Fair cache allocation for data-parallel workloads. In Proceedings of the 2017 ACM International Conference on Management of Data, pages 219-234, 2017. Google Scholar
  26. Euiwoong Lee. APX-hardness of maximizing Nash social welfare with indivisible items. Information Processing Letters, 122:17-20, 2017. Google Scholar
  27. Peter McGlaughlin and Jugal Garg. Improving Nash social welfare approximations. J. Artif. Intell. Res., 68:225-245, 2020. Google Scholar
  28. H. Moulin. Fair Division and Collective Welfare. Mit Press. MIT Press, 2004. Google Scholar
  29. Benjamin Plaut and Tim Roughgarden. Almost envy-freeness with general valuations. SIAM Journal on Discrete Mathematics, 34(2):1039-1068, 2020. Google Scholar
  30. John Rawls. A theory of justice. Harvard university press, 2009. Google Scholar
  31. Herbert E Scarf. The core of an N person game. Econometrica: Journal of the Econometric Society, pages 50-69, 1967. Google Scholar
  32. Hugo Steinhaus. The problem of fair division. Econometrica, 16:101-104, 1948. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail