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Possible and Necessary Allocations Under Serial Dictatorship with Incomplete Preference Lists

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Algorithmic Decision Theory (ADT 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10576))

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Abstract

We study assignment problems in a model where agents have strict preferences over objects, allowing preference lists to be incomplete. We investigate the questions whether an agent can obtain or necessarily obtains a given object under serial dictatorship. We prove that both problems are computationally hard even if agents have preference lists of length at most 3; by contrast, we give linear-time algorithms for the case where preference lists are of length at most 2. We also study a capacitated version of these problems where objects come in several copies.

This work was supported by VEGA grants 1/0344/14 and 1/0142/15 from the Slovak Scientific Grant Agency and grant APVV-15-0091 (Cechlárová), by OTKA grants K108383 (Fleiner) and K108947 (Schlotter), and the MTA-ELTE Egerváry Research Group (Fleiner). The authors gratefully acknowledge the support of COST Action IC1205 Computational Social Choice.

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Notes

  1. 1.

    Note that the modifications in the reduction given in the proof of Theorem 6 that prove the hardness of 2-cpos \((I,a,\emptyset )\) and 2-cnec(I, a, f(a)) still work after the application of Lemma 4.

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Authors and Affiliations

  1. Faculty of Science, Institute of Mathematics, P.J. Šafárik University, Jesenná 5, Košice, Slovakia

    Katarína Cechlárová

  2. Budapest University of Technology and Economics, Magyar tudósok körútja 2, 1117, Budapest, Hungary

    Tamás Fleiner & Ildikó Schlotter

Authors
  1. Katarína Cechlárová
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  2. Tamás Fleiner
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  3. Ildikó Schlotter
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Corresponding authors

Correspondence to Katarína Cechlárová or Ildikó Schlotter .

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Editors and Affiliations

  1. Heinrich Heine University, Düsseldorf, Germany

    Jörg Rothe

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Cechlárová, K., Fleiner, T., Schlotter, I. (2017). Possible and Necessary Allocations Under Serial Dictatorship with Incomplete Preference Lists. In: Rothe, J. (eds) Algorithmic Decision Theory. ADT 2017. Lecture Notes in Computer Science(), vol 10576. Springer, Cham. https://doi.org/10.1007/978-3-319-67504-6_21

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  • DOI: https://doi.org/10.1007/978-3-319-67504-6_21

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-319-67504-6

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