The Complexity of Manipulative Attacks in Nearly Single-Peaked Electorates

Details The Complexity of Manipulative Attacks in Nearly Single-Peaked Electorates The Complexity of Manipulative Attacks in Nearly Single-Peaked Electorates

2011-05-25

arxiv.org/abs/1105.5032v1

Computer Science

Computer Science and Game Theory

35 pages, also appears as URCS-TR-2011-968

Scientific paper

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.

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