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Multi-winner Approval Voting with Grouped Voters

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Combinatorial Optimization and Applications (COCOA 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14462))

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Abstract

We consider the general case of approval-based committee elections, where some attributes divide the voters into diverse groups which vary in size. This scenario occurs in applications like the presidential election, where voters come from different parties, or the student board election at a university with students from different schools. However, all existing committee election rules either are derived for the single-group case, or neglect the welfare of groups with few votes. Therefore, new voting rules are needed for this setting. In this paper, We propose two natural axioms for this setting, namely, small group benefited representation (SGBR) and large group benefited representation (LGBR). SGBR requires that if the committee size exceeds the number of groups, at least one candidate approved by each group is in the winning committee. LGBR requires that the winning committee must have at least as many candidates approved by a large group as by a small group. Based on the axioms, we propose three models and investigate parameterized complexity of the models with respect to various parameters. We show that all models are fixed-parameter tractable (FPT) when parameterized by the number n of votes, whereas they become fixed-parameter intractable when parameterized by the size k of the committee or d of the satisfaction bound.

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References

  1. 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)

    Article  MathSciNet  Google Scholar 

  2. Aziz, H., Gaspers, S., Gudmundsson, J., Mackenzie, S., Mattei, N., Walsh, T.: Computational aspects of multi-winner approval voting. In: AAMAS 2015, pp. 107–115 (2015)

    Google Scholar 

  3. Baumeister, D., Dennisen, S., Rey, L.: Winner determination and manipulation in minisum and minimax committee elections. In: ADT 2015. vol. 9346, pp. 469–485 (2015)

    Google Scholar 

  4. Bei, X., Liu, S., Poon, C.K., Wang, H.: Candidate selections with proportional fairness constraints. Auton. Agent. Multi-Agent Syst. 36(1), 5 (2022)

    Article  Google Scholar 

  5. Brams, S.: Mathematics and democracy: designing better voting and fair-division procedures. Math. Comput. Modell. 48(9–10), 1666–1670 (2008)

    Article  Google Scholar 

  6. Brams, S., Kilgour, D.M., Sanver, M.R.: A minimax procedure for electing committees. Public Choice 132, 401–420 (2007)

    Article  Google Scholar 

  7. Brams, S.J., Kilgour, D.M.: Satisfaction approval voting. In: Fara, R., Leech, D., Salles, M. (eds.) Voting Power and Procedures. SCW, pp. 323–346. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-05158-1_18

    Chapter  Google Scholar 

  8. Brandt, F., Conitzer, V., Endriss, U., Lang, J., Procaccia, A.D. (eds.): Handbook of Computational Social Choice. Cambridge University Press, Cambridge (2016)

    Google Scholar 

  9. Bredereck, R., Chen, J., Faliszewski, P., Guo, J., Niedermeier, R., Woeginger, G.J.: Parameterized algorithmics for computational social choice: Nine research challenges. Tsinghua Sci. Technol. 19(4), 358–373 (2014)

    Article  MathSciNet  Google Scholar 

  10. Bredereck, R., Faliszewski, P., Igarashi, A., Lackner, M., Skowron, P.: Multiwinner elections with diversity constraints. In: Proceedings of the 32nd AAAI Conference on Artificial Intelligence, pp. 933–940 (2018)

    Google Scholar 

  11. Celis, L.E., Huang, L., Vishnoi, N.K.: Multiwinner voting with fairness constraints. In: Proceedings of the 27th International Joint Conference on Artificial Intelligence, pp. 144–151 (2018)

    Google Scholar 

  12. Chamberlin, J., Courant, P.: Representative deliberations and representative decisions: proportional representation and the Borda rule. Am. Polit. Sci. Rev. 77(3), 718–733 (1983)

    Article  Google Scholar 

  13. Conitzer, V.: Making decisions based on the preferences of multiple agents. Commun. ACM 53(3), 84–94 (2010)

    Article  MathSciNet  Google Scholar 

  14. Downey, R., Fellows, M.: Parameterized Complexity. Springer Science & Business Media (2012)

    Google Scholar 

  15. Faliszewski, P., Talmon, N.: Between proportionality and diversity: balancing district sizes under the Chamberlin-courant rule. In: Proceedings of the 17th International Conference on Autonomous Agents and Multi-Agent Systems, pp. 14–22 (2018)

    Google Scholar 

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

    Google Scholar 

  17. Fishburn, P.: Axioms for approval voting: direct proof. J. Econ. Theory 19(1), 180–185 (1978)

    Article  MathSciNet  Google Scholar 

  18. Ianovski, E.: Electing a committee with dominance constraints. Ann. Oper. Res. 318(2), 985–1000 (2022)

    Article  MathSciNet  Google Scholar 

  19. Kilgour, D.M., Marshall, E.: Approval balloting for fixed-size committees. Electoral systems: paradoxes, assumptions, and procedures, pp. 305–326 (2012)

    Google Scholar 

  20. Kilgour, M.: Approval balloting for multi-winner elections. In: Handbook on Approval Voting, pp. 105–124. Springer (2010). https://doi.org/10.1007/978-3-642-02839-7_6

  21. Lang, J., Skowron, P.: Multi-attribute proportional representation. Artif. Intell. 263, 74–106 (2018)

    Article  MathSciNet  Google Scholar 

  22. LeGrand, R., Markakis, E., Mehta, A.: Some results on approximating the minimax solution in approval voting. In: AAMAS 2007, p. 198 (2007)

    Google Scholar 

  23. Lenstra, H.: Integer programming with a fixed number of variables. Math. Oper. Res. 8(4), 538–548 (1983)

    Article  MathSciNet  Google Scholar 

  24. Obraztsova, S., Zick, Y., Elkind, E.: On manipulation in multi-winner elections based on scoring rules. In: AAMAS 2013, pp. 359–366 (2013)

    Google Scholar 

  25. Procaccia, A.D., Rosenschein, J.S., Zohar, A.: On the complexity of achieving proportional representation. Soc. Choice Welfare 30(3), 353–362 (2008)

    Article  MathSciNet  Google Scholar 

  26. Talmon, N.: Structured proportional representation. Theoret. Comput. Sci. 708, 58–74 (2018)

    Article  MathSciNet  Google Scholar 

  27. Thiele, T.N.: Om flerfoldsvalg. Oversigt over det Kongelige Danske Videnskabernes Selskabs Forhandlinger 1895, 415–441 (1895)

    Google Scholar 

  28. Zwicker, W.S.: Introduction to the theory of voting. In: Handbook of Computational Social Choice, pp. 23–56. Cambridge University Press (2016)

    Google Scholar 

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Correspondence to Yinghui Wen or Jiong Guo .

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Wen, Y., Song, C., Zhou, A., Guo, J. (2024). Multi-winner Approval Voting with Grouped Voters. In: Wu, W., Guo, J. (eds) Combinatorial Optimization and Applications. COCOA 2023. Lecture Notes in Computer Science, vol 14462. Springer, Cham. https://doi.org/10.1007/978-3-031-49614-1_20

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  • DOI: https://doi.org/10.1007/978-3-031-49614-1_20

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-49613-4

  • Online ISBN: 978-3-031-49614-1

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