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A social choice approach to ordinal group activity selection

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  • Darmann, Andreas

Abstract

We consider the situation in which group activities need to be organized for a set of agents when each agent can take part in at most one activity. The agents’ preferences depend both on the activity and the number of participants in that activity. In particular, the preferences are given by means of strict orders over pairs “(activity, group size)”, including the possibility “do nothing”. Our goal will be to assign agents to activities on basis of their preferences, the minimum requirement being that no agent prefers doing nothing, i.e., not taking part in any activity at all. Taking a social choice perspective, we aim at establishing such an assignment by two approaches. On the one hand, we use k-approval and Borda scores, and we apply the Condorcet criterion on the other hand. We analyze the computational complexity involved in finding a desired assignment, with focus on two natural special cases of agents’ preferences which allow for some positive complexity results.

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  • Darmann, Andreas, 2018. "A social choice approach to ordinal group activity selection," Mathematical Social Sciences, Elsevier, vol. 93(C), pages 57-66.
    • Handle: RePEc:eee:matsoc:v:93:y:2018:i:c:p:57-66
    DOI: 10.1016/j.mathsocsci.2018.01.005
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    1. Dinko Dimitrov & Peter Borm & Ruud Hendrickx & Shao Sung, 2006. "Simple Priorities and Core Stability in Hedonic Games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(2), pages 421-433, April.
    2. Ballester, Coralio, 2004. "NP-completeness in hedonic games," Games and Economic Behavior, Elsevier, vol. 49(1), pages 1-30, October.
    3. Darmann, Andreas, 2013. "How hard is it to tell which is a Condorcet committee?," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 282-292.
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    7. Christian Klamler & Ulrich Pferschy, 2007. "The traveling group problem," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 29(3), pages 429-452, October.
    8. Andreas Darmann, 2018. "Stable and Pareto optimal group activity selection from ordinal preferences," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(4), pages 1183-1209, November.
    9. Andreas Darmann, 2016. "It is difficult to tell if there is a Condorcet spanning tree," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 84(1), pages 93-104, August.
    10. Barış Kaymak & M. Remzi Sanver, 2003. "Sets of alternatives as Condorcet winners," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 20(3), pages 477-494, June.
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    1. Andreas Darmann, 2018. "Stable and Pareto optimal group activity selection from ordinal preferences," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(4), pages 1183-1209, November.
    2. Andreas Darmann & Janosch Döcker & Britta Dorn & Sebastian Schneckenburger, 2022. "Simplified group activity selection with group size constraints," International Journal of Game Theory, Springer;Game Theory Society, vol. 51(1), pages 169-212, March.

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