The Complexity of Fully Proportional Representation for Single-Crossing Electorates

  • Piotr Skowron
  • Lan Yu
  • Piotr Faliszewski
  • Edith Elkind
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8146)

Abstract

We study the complexity of winner determination in single-crossing elections under two classic fully proportional representation rules—Chamberlin–Courant’s rule and Monroe’s rule. Winner determination for these rules is known to be NP-hard for unrestricted preferences. We show that for single-crossing preferences this problem admits a polynomial-time algorithm for Chamberlin–Courant’s rule, but remains NP-hard for Monroe’s rule. Our algorithm for Chamberlin–Courant’s rule can be modified to work for elections with bounded single-crossing width. To circumvent the hardness result for Monroe’s rule, we consider single-crossing elections that satisfy an additional constraint, namely, ones where each candidate is ranked first by at least one voter (such elections are called narcissistic). For single-crossing narcissistic elections, we provide an efficient algorithm for the egalitarian version of Monroe’s rule.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Piotr Skowron
    • 1
  • Lan Yu
    • 2
  • Piotr Faliszewski
    • 3
  • Edith Elkind
    • 2
  1. 1.University of WarsawPoland
  2. 2.Nanyang Technological UniversitySingapore
  3. 3.AGH University of Science and TechnologyPoland

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