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On the Parameterized Complexity of Party Nominations

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Algorithmic Decision Theory (ADT 2019)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11834))

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Abstract

Consider a fixed voting rule . In the Possible President problem, we are given an election where the candidates are partitioned into parties, and the problem is to determine if, given a party , it is possible for every party to nominate a candidate such that the nominee from is a winner of the election that is obtained by restricting the votes to the nominated candidates. In previous work on this problem, proposed by [10], it was established that Possible President is NP-hard even when the voting rule is Plurality and the election is restricted to single-peaked votes. In this contribution, we initiate a study of the parameterized complexity of the problem. Our main result is that for a natural choice of parameter (namely the number of parties), the problem is W[2]-hard in general but is FPT on the 1D-Euclidean domain. On the other hand, if we parameterize by the size of the largest party, we encounter para-NP-hardness even on profiles that are both single-peaked and single-crossing. This strengthens previously established hardness results. We also show a polynomial time result for the related Necessary President problem on single-crossing elections.

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Notes

  1. 1.

    In this case, note that the outcome of the election does not depend on who is nominated.

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Authors and Affiliations

  1. Indian Institute of Technology, Gandhinagar, India

    Neeldhara Misra

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  1. Neeldhara Misra
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Correspondence to Neeldhara Misra .

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Editors and Affiliations

  1. Fuqua School of Business, Duke University, Durham, NC, USA

    Saša Pekeč

  2. Florida Institute for Human and Machine Cognition (IHMC), Pensacola, FL, USA

    Kristen Brent Venable

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Misra, N. (2019). On the Parameterized Complexity of Party Nominations. In: Pekeč, S., Venable, K.B. (eds) Algorithmic Decision Theory. ADT 2019. Lecture Notes in Computer Science(), vol 11834. Springer, Cham. https://doi.org/10.1007/978-3-030-31489-7_8

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  • DOI: https://doi.org/10.1007/978-3-030-31489-7_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-31488-0

  • Online ISBN: 978-3-030-31489-7

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