## Average-case tractability of manipulation in voting via the fraction of manipulators (2007)

Venue: | In Proc. of AAMAS |

Citations: | 22 - 2 self |

### BibTeX

@INPROCEEDINGS{Procaccia07average-casetractability,

author = {Ariel D. Procaccia and Jeffrey S. Rosenschein},

title = {Average-case tractability of manipulation in voting via the fraction of manipulators},

booktitle = {In Proc. of AAMAS},

year = {2007}

}

### OpenURL

### Abstract

Recent results have established that a variety of voting rules are computationally hard to manipulate in the worst-case; this arguably provides some guarantee of resistance to manipulation when the voters have bounded computational power. Nevertheless, it has become apparent that a truly dependable obstacle to manipulation can only be provided by voting rules that are average-case hard to manipulate. In this paper, we analytically demonstrate that, with respect to a wide range of distributions over votes, the coalitional manipulation problem can be decided with overwhelming probability of success by simply considering the ratio between the number of truthful and untruthful voters. Our results can be employed to significantly focus the search for that elusive average-case-hard-to-manipulate voting rule, but at the same time these results also strengthen the case against the existence of such a rule. 1

### Citations

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(Show Context)
Citation Context ...hat the probability that a sum of random variables obtains values in a very small segment is very small, as long as the variance of the random variables is nonzero. Theorem 2 (Central Limit Theorem). =-=[8]-=- Let X 1 , X 2 , . . . , X N , . . . be a sequence of independent discrete random variables. For each i, denote the mean and variance of Xi by µ i and σi , respectively, and assume that ∑N N→∞ i=1 σi ... |

351 |
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(Show Context)
Citation Context ...socially desirable outcome to emerge from an election, voters should reveal their true preferences — but precluding manipulation is impossible in general. The celebrated Gibbard-Satterthwaite Theorem =-=[13]-=- states that, with any reasonable voting rule (a function that determines the outcome of the election, given the voters’ preferences), there are elections where some of the voters can benefit by votin... |

137 | Single Transferable Vote Resists Strategic Voting. Social Choice and Welfare 8(4):341–354
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(Show Context)
Citation Context ... in principle a voter may lie in order to improve its position, determining if it is possible in practice, given a specific setting, may be a computationally hard problem. Indeed, Bartholdi and Orlin =-=[2]-=- demonstrated that the important Single Transferable Vote (STV) voting rule is N P-hard to manipulate. More recent results imply that it is possible to make simple voting rules, which could otherwise ... |

105 | Universal Voting Protocol Tweaks to Make Manipulation Hard
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(Show Context)
Citation Context ...ng rule is N P-hard to manipulate. More recent results imply that it is possible to make simple voting rules, which could otherwise be manipulated efficiently, hard to manipulate by adding a preround =-=[6]-=-. Other research shows that many voting rules are N P-hard to manipulate by a coalition of weighted voters [5, 4]; these results hold even when the number of candidates is constant, though the number ... |

87 | Junta Distributions and the AverageCase Complexity of Manipulating Elections
- Procaccia, Rosenschein
- 2007
(Show Context)
Citation Context ... reasonable to hope for a voting rule 1that has this property at least under certain interesting distributions. Sadly, two recent papers presented evidence to the contrary. Procaccia and Rosenschein =-=[12]-=- defined the notion of junta distribution, and argued that if an algorithm can usually decide the manipulation problem with respect to a junta distribution, the same algorithm would usually succeed wi... |

73 | Nonexistence of Voting Rules That Are Usually Hard to Manipulate
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(Show Context)
Citation Context ...ing rule is a scoring rule (see Section 2 for a formal definition). However, the relation between junta distributions and other distributions is not as yet formally established. Conitzer and Sandholm =-=[7]-=- proposed a different approach: they demonstrated that if an instance of the manipulation problem has certain properties, it is easy to decide. Further, it was empirically shown that, in a variety of ... |

72 | Complexity of manipulating elections with few candidates
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(Show Context)
Citation Context ...which could otherwise be manipulated efficiently, hard to manipulate by adding a preround [6]. Other research shows that many voting rules are N P-hard to manipulate by a coalition of weighted voters =-=[5, 4]-=-; these results hold even when the number of candidates is constant, though the number of manipulative voters must be unbounded. The abovementioned computational results all imply worst-case hardness.... |

37 | How Many Candidates Are Needed to Make Elections Hard to Manipulate
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(Show Context)
Citation Context ...which could otherwise be manipulated efficiently, hard to manipulate by adding a preround [6]. Other research shows that many voting rules are N P-hard to manipulate by a coalition of weighted voters =-=[5, 4]-=-; these results hold even when the number of candidates is constant, though the number of manipulative voters must be unbounded. The abovementioned computational results all imply worst-case hardness.... |

35 |
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(Show Context)
Citation Context ...gating the preferences of heterogeneous, self-interested agents. For instance, voting has been employed to help agents reach an agreement regarding joint plans, schedules [10], and recommended movies =-=[9]-=-. Unfortunately, for a socially desirable outcome to emerge from an election, voters should reveal their true preferences — but precluding manipulation is impossible in general. The celebrated Gibbard... |

29 | Instance complexity
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Citation Context ...s. Although it can be argued that these results demonstrate some measure of resistance to manipulation, by no means do they preclude it. An N P-hard problem has an infinite number of “hard instances” =-=[11]-=-, but it may still be the case that most instances are “easy”. In our setting, this means that a strategic voter might usually be able to determine whether or not to reveal its true preferences. There... |

24 |
An automated meeting scheduling system that utilizes user preferences
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(Show Context)
Citation Context ...ten used as a method of aggregating the preferences of heterogeneous, self-interested agents. For instance, voting has been employed to help agents reach an agreement regarding joint plans, schedules =-=[10]-=-, and recommended movies [9]. Unfortunately, for a socially desirable outcome to emerge from an election, voters should reveal their true preferences — but precluding manipulation is impossible in gen... |

15 |
How Large Should a Coalition Be to Manipulate an Election
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(Show Context)
Citation Context ...d to focus the search for such a rule, should it exist. Some recent research in economics has independently recognized that when the fraction of manipulators is small, manipulation is rarely possible =-=[14, 1]-=-. However, these papers consider only variations on the uniform distribution over possible elections; this is plausible from the economist’s point of view, but in computer science we can preclude aver... |