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Core-Stable Committees Under Restricted Domains

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Web and Internet Economics (WINE 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13778))

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Abstract

We study the setting of committee elections, where a group of individuals needs to collectively select a given-size subset of available objects. This model is relevant for a number of real-life scenarios including political elections, participatory budgeting, and facility-location. We focus on the core—the classic notion of proportionality, stability and fairness. We show that for a number of restricted domains including voter-interval, candidate-interval, single-peaked, and single-crossing preferences the core is non-empty and can be found in polynomial time. We show that the core might be empty for strict top-monotonic preferences, yet we introduce a relaxation of this class, which guarantees non-emptiness of the core. Our algorithms work both in the randomized and discrete models. We also show that the classic known proportional rules do not return committees from the core even for the most restrictive domains among those we consider (in particular for 1D-Euclidean preferences). We additionally prove a number of structural results that give better insights into the nature of some of the restricted domains, and which in particular give a better intuitive understanding of the class of top-monotonic preferences.

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Notes

  1. 1.

    Typically a voting rule would return a single winning committee, but ties are possible.

References

  1. Aziz, H., Bogomolnaia, A., Moulin, H.: Fair mixing: the case of dichotomous preferences. In: EC-2019, pp. 753–781 (2019)

    Google Scholar 

  2. Aziz, H., Brill, M., Conitzer, V., Elkind, E., Freeman, R., Walsh, T.: Justified representation in approval-based committee voting. Soc. Choice Welfare 48(2), 461–485 (2017). https://doi.org/10.1007/s00355-016-1019-3

    Article  MathSciNet  MATH  Google Scholar 

  3. Aziz, H., Elkind, E., Faliszewski, P., Lackner, M., Skowron, P.: The Condorcet principle for multiwinner elections: from shortlisting to proportionality. In: IJCAI-2017, pp. 84–90, August 2017

    Google Scholar 

  4. Aziz, H., Lee, B.: The expanding approvals rule: improving proportional representation and monotonicity. Soc. Choice Welfare 54(1), 1–45 (2020). https://doi.org/10.1007/s00355-019-01208-3

    Article  MathSciNet  MATH  Google Scholar 

  5. Barberà, S., Moreno, B.: Top monotonicity: a common root for single peakedness, single crossing and the median voter result. Games Econom. Behav. 73(2), 345–359 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  6. Black, D.: On the rationale of group decision-making. J. Polit. Econ. 56(1), 23–34 (1948)

    Article  Google Scholar 

  7. Brandt, F.: Rolling the dice: recent results in probabilistic social choice. In: Endriss, U. (ed.) Trends in Computational Social Choice, pp. 3–26. AI Access (2017)

    Google Scholar 

  8. Brill, M., Gölz, P., Peters, D., Schmidt-Kraepelin, U., Wilker, K.: Approval-based apportionment. In: AAAI-2020, pp. 1854–1861 (2020)

    Google Scholar 

  9. Burdges, J., et al.: Overview of Polkadot and its design considerations. arXiv preprint arXiv:2005.13456 (2020)

  10. Cevallos, A., Stewart, A.: A verifiably secure and proportional committee election rule. arXiv preprint arXiv:2004.12990 (2020)

  11. Chalkiadakis, G., Elkind, E., Wooldridge, M.: Computational aspects of cooperative game theory. In: Synthesis Lectures on Artificial Intelligence and Machine Learning, vol. 5, no. 6, pp. 1–168 (2011)

    Google Scholar 

  12. Cheng, Y., Jiang, Z., Munagala, K., Wang, K.: Group fairness in committee selection. In: EC-2019, pp. 263–279 (2019)

    Google Scholar 

  13. Dummett, M.: Voting Procedures. Oxford University Press, Oxford (1984)

    Google Scholar 

  14. Elkind, E., Faliszewski, P., Skowron, P.: A characterization of the single-peaked single-crossing domain. Soc. Choice Welfare 54, 167–181 (2020). https://doi.org/10.1007/s00355-019-01216-3

    Article  MathSciNet  MATH  Google Scholar 

  15. Elkind, E., Faliszewski, P., Skowron, P., Slinko, A.: Properties of multiwinner voting rules. Soc. Choice Welfare 48(3), 599–632 (2017). https://doi.org/10.1007/s00355-017-1026-z

    Article  MathSciNet  MATH  Google Scholar 

  16. Elkind, E., Lackner, M.: Structure in dichotomous preferences. In: IJCAI-2015, pp. 2019–2025 (2015)

    Google Scholar 

  17. Elkind, E., Lackner, M., Peters, D.: Structured preferences. In: Trends in Computational Social Choice, pp. 187–207 (2017)

    Google Scholar 

  18. Fain, B., Goel, A., Munagala, K.: The core of the participatory budgeting problem. In: Cai, Y., Vetta, A. (eds.) WINE 2016. LNCS, vol. 10123, pp. 384–399. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-54110-4_27

    Chapter  Google Scholar 

  19. Fain, B., Munagala, K., Shah, N.: Fair allocation of indivisible public goods. In: Proceedings of the 2018 ACM Conference on Economics and Computation, pp. 575–592 (2018). Extended version. arXiv:1805.03164

  20. Faliszewski, P., Skowron, P., Slinko, A., Talmon, N.: Multiwinner voting: a new challenge for social choice theory. In: Endriss, U. (ed.) Trends in Computational Social Choice, pp. 27–47. AI Access (2017)

    Google Scholar 

  21. Farahani, R.Z., Hekmatfar, M. (eds.): Facility Location: Concepts, Models, Algorithms and Case Studies. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-7908-2151-2

    Book  Google Scholar 

  22. Jiang, Z., Munagala, K., Wang, K.: Approximately stable committee selection. In: STOC-2020, pp. 463–472 (2020)

    Google Scholar 

  23. Lackner, M., Skowron, P.: Approval-based committee voting: axioms, algorithms, and applications. Technical report. arXiv:2007.01795 [cs.GT], arXiv.org (2020)

  24. Magiera, K., Faliszewski, P.: Recognizing top-monotonic preference profiles in polynomial time. J. Artif. Intell. Res. 66, 57–84 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  25. Mirrlees, J.: An exploration in the theory of optimal income taxation. Rev. Econ. Stud. 38, 175–208 (1971)

    Article  MATH  Google Scholar 

  26. Osborne, J.M., Rubinstein, A.: A Course in Game Theory, vol. 1. The MIT Press, Cambridge (1994)

    MATH  Google Scholar 

  27. Peters, D., Skowron, P.: Proportionality and the limits of welfarism. In: EC-2020, pp. 793–794 (2020). Extended version. arXiv:1911.11747

  28. Pierczyński, G., Skowron, P.: Core-stable committees under restricted domains (2021). https://doi.org/10.48550/ARXIV.2108.01987. https://arxiv.org/abs/2108.01987

  29. Roberts, K.W.S.: Voting over income tax schedules. J. Public Econ. 8(3), 329–340 (1977)

    Article  Google Scholar 

  30. Sánchez-Fernández, L., et al.: Proportional justified representation. In: Proceedings of the 31st AAAI Conference on Artificial Intelligence (AAAI-2017), pp. 670–676 (2017)

    Google Scholar 

  31. Skowron, P., Faliszewski, P., Lang, J.: Finding a collective set of items: from proportional multirepresentation to group recommendation. Artif. Intell. 241, 191–216 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  32. Skowron, P., Lackner, M., Brill, M., Peters, D., Elkind, E.: Proportional rankings. In: IJCAI-2017, pp. 409–415 (2017)

    Google Scholar 

  33. Srinivasan, A.: Distributions on level-sets with applications to approximation algorithms. In: FOCS-2001, pp. 588–597 (2001)

    Google Scholar 

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Authors and Affiliations

  1. University of Warsaw, Warsaw, Poland

    Grzegorz Pierczyński & Piotr Skowron

Authors
  1. Grzegorz Pierczyński
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  2. Piotr Skowron
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Correspondence to Grzegorz Pierczyński .

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Editors and Affiliations

  1. Aarhus University, Aarhus, Denmark

    Kristoffer Arnsfelt Hansen

  2. Tsinghua University, Beijing, China

    Tracy Xiao Liu

  3. Rotman School of Management, University of Toronto, Toronto, ON, Canada

    Azarakhsh Malekian

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Pierczyński, G., Skowron, P. (2022). Core-Stable Committees Under Restricted Domains. In: Hansen, K.A., Liu, T.X., Malekian, A. (eds) Web and Internet Economics. WINE 2022. Lecture Notes in Computer Science, vol 13778. Springer, Cham. https://doi.org/10.1007/978-3-031-22832-2_18

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  • DOI: https://doi.org/10.1007/978-3-031-22832-2_18

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-22831-5

  • Online ISBN: 978-3-031-22832-2

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