Dichotomy for voting systems

  • Authors:

  • Edith Hemaspaandra;Lane A. Hemaspaandra

  • Affiliations:

  • Department of Computer Science, Rochester Institute of Technology, Rochester, NY 14623, USA;Department of Computer Science, University of Rochester, Rochester, NY 14627, USA

  • Venue:
  • Journal of Computer and System Sciences
  • Year:
  • 2007

Quantified Score

Hi-index 0.03

Visualization

Abstract

Scoring protocols are a broad class of voting systems. Each is defined by a vector (@a"1,@a"2,...,@a"m), @a"1=@a"2=...=@a"m, of integers such that each voter contributes @a"1 points to his/her first choice, @a"2 points to his/her second choice, and so on, and any candidate receiving the most points is a winner. What is it about scoring-protocol election systems that makes some have the desirable property of being NP-complete to manipulate, while others can be manipulated in polynomial time? We find the complete, dichotomizing answer: Diversity of dislike. Every scoring-protocol election system having two or more point values assigned to candidates other than the favorite-i.e., having @?{@a"i|2==2-is NP-complete to manipulate. Every other scoring-protocol election system can be manipulated in polynomial time. In effect, we show that-other than trivial systems (where all candidates alway tie), plurality voting, and plurality voting's transparently disguised translations-every scoring-protocol election system is NP-complete to manipulate.