Copeland Voting Fully Resists Constructive Control

  • Authors:

  • Piotr Faliszewski;Edith Hemaspaandra;Lane A. Hemaspaandra;Jörg Rothe

  • Affiliations:

  • Dept. of Computer Science, University of Rochester, Rochester, USA NY 14627;Dept. of Computer Science, RIT, Rochester, USA NY 14623;Dept. of Computer Science, University of Rochester, Rochester, USA NY 14627;Inst. für Informatik, Universität Düsseldorf, Düsseldorf, Germany 40225

  • Venue:
  • AAIM '08 Proceedings of the 4th international conference on Algorithmic Aspects in Information and Management
  • Year:
  • 2008

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Abstract

Control and bribery are settings in which an external agent seeks to influence the outcome of an election. Faliszewski et al. [9] proved that Llull voting (which is here denoted by Copeland1) and a variant (here denoted by Copeland0) of Copeland voting are computationally resistant to many, yet not all, types of constructive control and that they also provide broad resistance to bribery. We study a parameterized version of Copeland voting, denoted by Copeland驴, where the parameter 驴is a rational number between 0 and 1 that specifies how ties are valued in the pairwise comparisons of candidates in Copeland elections. For each rational 驴, 0 驴驴is computationally vulnerable to control in that scenario (i.e., we give a P-time algorithm that determines whether control is possible, and if so, determines exactly how to exert the control) or we prove that Copeland驴is computationally resistant to control in that scenario (i.e., we prove that control problem to be NP-hard). In particular, we prove that Copeland0.5, the system commonly referred to as "Copeland voting," provides full resistance to constructive control. Among systems with a polynomial-time winner problem, this is the first natural election system proven to have full resistance to constructive control. Looking at rational 驴, 0 驴驴(previously only Copeland0and Copeland1had been studied), and we introduce and obtain fixed-parameter tractability results even in a new, more flexible model of control (that we dub "extended control").