The complexity of manipulative attacks in nearly single-peaked electorates

  • Authors:

  • Piotr Faliszewski;Edith Hemaspaandra;Lane A. Hemaspaandra

  • Affiliations:

  • Department of Computer Science, AGH Univ. of Science and Technology, Kraków, Poland;Department of Computer Science, Rochester Institute of Technology, Rochester, NY 14623, USA;Department of Computer Science, University of Rochester, Rochester, NY 14627, USA

  • Venue:
  • Artificial Intelligence
  • Year:
  • 2014

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Abstract

Many electoral control and manipulation problems-which we will refer to in general as ''manipulative actions'' problems-are NP-hard in the general case. It has recently been noted that many of these problems fall into polynomial time if the electorate is single-peaked, i.e., is polarized along some axis/issue. However, real-world electorates are not truly single-peaked. There are usually some mavericks, and so real-world electorates tend merely to be nearly single-peaked. This paper studies the complexity of manipulative-action algorithms for elections over nearly single-peaked electorates. We do this for many notions of nearness and for a broad range of election systems. We provide instances where even one maverick jumps the manipulative-action complexity up to NP-hardness, but we also provide many instances where some number of mavericks can be tolerated without increasing the manipulative-action complexity.