How hard is it to control a group?
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We consider group identification models in which the aggregation of individual opinions concerning who is qualified in a given society determines the set of socially qualified persons. In this setting, we study the extent to which social qualification can be changed when societies expand, shrink, or partition themselves. The answers we provide are with respect to the computational complexity of the corresponding control problems and fully cover the class of consent aggregation rules introduced by Samet and Schmeidler (J Econ Theory, 110(2):213–233, 2003) as well as procedural rules for group identification. We obtain both polynomial-time solvability results and NP-hardness results. In addition, we also study these problems from the parameterized complexity perspective, and obtain some fixed-parameter tractability results.
KeywordsGroup identification Consent rules Procedural rules Computational complexity Parameterized complexity Control
We thank Shao-Chin Sung and the anonymous reviewers of JAAMAS and COMSOC 2016 for their valuable comments.
- 1.Aziz, H., Gaspers, S., Gudmundsson, J., Mackenzie, S., Mattei, N., & Walsh, T. (2015). Computational aspects of multi-winner approval voting. In AAMAS (pp. 107–115).Google Scholar
- 2.Bartholdi, J. J., III, Tovey, C. A., & Trick, M. A. (1992). How hard is it to control an election? Mathematical and Computer Modelling, 16(8–9), 27–40.Google Scholar
- 3.Baumeister, D., Erdélyi, G., Hemaspaandra, E., Hemaspaandra, L. A., & Rothe, J. (2010). Computational aspects of approval voting, chap. 10. In Handbook on approval voting (pp. 199–251). Berlin: Springer.Google Scholar
- 6.Cook, S. A. (1971). The complexity of theorem-proving procedures. In STOC (pp. 151–158).Google Scholar
- 8.Dimitrov, D. (2011). The social choice approach to group identification. In Consensual processes (pp. 123–134).Google Scholar
- 12.Elkind, E., & Lackner, M. (2015) Structure in dichotomous preferences. In IJCAI (pp. 2019–2025).Google Scholar
- 13.Erdélyi, G., Reger, C., & Yang, Y. (2017). The complexity of bribery and control in group identification. In AAMAS (pp. 1142–1150).Google Scholar
- 14.Erdélyi, G., Reger, C., & Yang, Y. (2017). Complexity of group identification with partial information. In ADT (pp. 182–196).Google Scholar
- 16.Faliszewski, P., & Rothe, J. (2016). Control and bribery in voting. In F. Brandt, V. Conitzer, U. Endriss, J. Lang, & A. Procaccia (Eds.), Handbook of computational social choice (Chap. 7, pp. 146–168). Cambridge: Cambridge University Press.Google Scholar
- 17.Faliszewski, P., Slinko, A., & Talmon, N. (2017). The complexity of multiwinner voting rules with variable number of winners. arXiv:1711.06641
- 27.Kilgour, D. M., & Marshall, E. (2012). Approval balloting for fixed-size committees. In D. S. Felsenthal & M. Machover (Eds.), Electoral systems, studies in choice and welfare (pp. 305–326). Berlin: Springer.Google Scholar
- 35.West, D. B. (2000). Introduction to graph theory. Englewood Cliffs: Prentice-Hall.Google Scholar
- 36.Yang, Y., & Guo, J. (2014). Controlling elections with bounded single-peaked width. In AAMAS (pp. 629–636).Google Scholar
- 37.Yang, Y., & Guo, J. (2015). How hard is control in multi-peaked elections: A parameterized study. In AAMAS (pp. 1729–1730).Google Scholar
- 39.Yang, Y., Wang, J. (2018). Multiwinner voting with restricted admissible sets: Complexity and strategyproofness. In IJCAI (to appear).Google Scholar