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Group Activity Selection from Ordinal Preferences

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Algorithmic Decision Theory (ADT 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9346))

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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 such 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. We take two different approaches to establish such an assignment: (i) by use of k-approval scores; (ii) considering stability concepts such as Nash and core stability.

For each of these approaches, we analyse the computational complexity involved in finding a desired assignment. Particular focus is laid on two natural special cases of agents? preferences which allow for positive complexity results.

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Notes

  1. 1.

    In fact, the case of 2-approval scores can be embedded in the 3-approval setting. The 2-approval case, however, allows for a very intuitive determination of an assignment of maximum score as described in the proof of Theorem 4.

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Acknowledgments

The author would like to thank Christian Klamler for helpful comments and Jérôme Lang for pointing towards research directions considered in this paper. In addition, the author would like to thank the anonymous referees for valuable comments that helped to improve the paper. Andreas Darmann was supported by the Austrian Science Fund (FWF): [P 23724-G11] ?Fairness and Voting in Discrete Optimization?.

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Authors and Affiliations

  1. University of Graz, Graz, Austria

    Andreas Darmann

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  1. Andreas Darmann
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Correspondence to Andreas Darmann .

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Editors and Affiliations

  1. University of New South Wales, Kensington, Australia

    Toby Walsh

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Darmann, A. (2015). Group Activity Selection from Ordinal Preferences. In: Walsh, T. (eds) Algorithmic Decision Theory. ADT 2015. Lecture Notes in Computer Science(), vol 9346. Springer, Cham. https://doi.org/10.1007/978-3-319-23114-3_3

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  • DOI: https://doi.org/10.1007/978-3-319-23114-3_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-23113-6

  • Online ISBN: 978-3-319-23114-3

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