The complexity of manipulative attacks in nearly single-peaked electorates

  • Authors:

  • Piotr Faliszewski;Edith Hemaspaandra;Lane A. Hemaspaandra

  • Affiliations:

  • AGH University of Science and Technology, Kraków, Poland;Rochester Institute of Technology, Rochester, NY;University of Rochester, Rochester, NY

  • Venue:
  • Proceedings of the 13th Conference on Theoretical Aspects of Rationality and Knowledge
  • Year:
  • 2011

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Abstract

Many electoral bribery, 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 to merely be nearly single-peaked. This paper studies the complexity of manipulative-action algorithms for elections over nearly single-peaked electorates, for various notions of nearness and various 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 a reasonable number of mavericks can be tolerated without increasing the manipulative-action complexity.