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Social Choice and Welfare

, Volume 48, Issue 2, pp 461–485 | Cite as

Justified representation in approval-based committee voting

  • Haris Aziz
  • Markus Brill
  • Vincent Conitzer
  • Edith Elkind
  • Rupert Freeman
  • Toby Walsh
Original Paper

Abstract

We consider approval-based committee voting, i.e. the setting where each voter approves a subset of candidates, and these votes are then used to select a fixed-size set of winners (committee). We propose a natural axiom for this setting, which we call justified representation (\(\mathrm {JR}\)). This axiom requires that if a large enough group of voters exhibits agreement by supporting the same candidate, then at least one voter in this group has an approved candidate in the winning committee. We show that for every list of ballots it is possible to select a committee that provides \(\mathrm {JR}\). However, it turns out that several prominent approval-based voting rules may fail to output such a committee. In particular, while Proportional Approval Voting (\(\mathrm {PAV}\)) always outputs a committee that provides \(\mathrm {JR}\), Sequential Proportional Approval Voting (\(\mathrm {SeqPAV}\)), which is a tractable approximation to \(\mathrm {PAV}\), does not have this property. We then introduce a stronger version of the \(\mathrm {JR}\) axiom, which we call extended justified representation (\(\mathrm {EJR}\)), and show that \(\mathrm {PAV}\) satisfies \(\mathrm {EJR}\), while other rules we consider do not; indeed, \(\mathrm {EJR}\) can be used to characterize \(\mathrm {PAV}\) within the class of weighted \(\mathrm {PAV}\) rules. We also consider several other questions related to \(\mathrm {JR}\) and \(\mathrm {EJR}\), including the relationship between \(\mathrm {JR}\)/\(\mathrm {EJR}\) and core stability, and the complexity of the associated computational problems.

Notes

Acknowledgements

The authors thank the anonymous reviewers of the Multidisciplinary Workshop on Advances in Preference Handling (MPREF 2014), and the Twenty-ninth AAAI Conference (AAAI 2015) for their helpful feedback on earlier versions of the paper. We further thank Svante Janson, Martin Lackner, Xavier Mora, and Piotr Skowron for valuable discussions. Brill, Conitzer, and Freeman were supported by NSF and ARO under Grants CCF-1101659, IIS-0953756, IIS-1527434, CCF-1337215, W911NF-12-1-0550, and W911NF-11-1-0332, by a Feodor Lynen research fellowship of the Alexander von Humboldt Foundation, and by COST Action IC1205 on Computational Social Choice. Aziz is supported by a Julius Career Award. Brill and Elkind were partially supported by ERC-StG 639945. Conitzer is supported by a Guggenheim Fellowship. Walsh also receives support from the Asian Office of Aerospace Research and Development (AOARD 124056) and the German Federal Ministry for Education and Research through the Alexander von Humboldt Foundation.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Haris Aziz
    • 1
  • Markus Brill
    • 2
  • Vincent Conitzer
    • 3
  • Edith Elkind
    • 2
  • Rupert Freeman
    • 3
  • Toby Walsh
    • 1
  1. 1.Data61, CSIRO and UNSW AustraliaSydneyAustralia
  2. 2.University of OxfordOxfordUK
  3. 3.Duke UniversityDurhamUSA

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