## Complexity of Judgment Aggregation: Safety of the Agenda (2010)

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Citations: | 12 - 10 self |

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@MISC{Endriss10complexityof,

author = {Ulle Endriss and Umberto Grandi and Daniele Porello},

title = {Complexity of Judgment Aggregation: Safety of the Agenda},

year = {2010}

}

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### Abstract

Aggregating the judgments of a group of agents regarding a set of interdependent propositions can lead to inconsistent outcomes. One of the parameters involved is the agenda, the set of propositions on which agents are asked to express an opinion. We introduce the problem of checking the safety of the agenda: for a given agenda, can we guarantee that judgment aggregation will never produce an inconsistent outcome for any aggregation procedure satisfying a given set of axioms? We prove several characterisation results, establishing necessary and sufficient conditions for the safety of the agenda for different combinations of the most important axioms proposed in the literature, and we analyse the computational complexity of checking whether a given agenda satisfies these conditions.

### Citations

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Citation Context ...e majority rule, which accepts a proposition for the collective judgment set if a majority of the individual agents do. Unfortunately, this can lead to a paradox (also known as the discursive dilemma =-=[8]-=-), as first Cite as: ���������� �� �������� ������������ ������ �� ��� ������� �� �������� �� ������ ��� �� �������� Proc.of9thInt.Conf.onAutonomous Agents and Multiagent Systems (AAMAS 2010)� ��� ���... |

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Citation Context ...ional complexity of the problem. 3.1 Safety of the Agenda: Problem Definition An important set of results in the literature on JA are possibility theorems, sometimes called “characterisation results” =-=[11, 9]-=-. Given some axioms as desiderata for the aggregation procedure (always including consistency), such a Axioms FΦ[WR,A,S,MI ] FΦ[WR,A,N,MN ] FΦ[WR,A,S] FΦ[WR,A,N] FΦ[WR,A,I] FΦ[A,S,M I ] Representation... |

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26 |
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Citation Context ...ional complexity of the problem. 3.1 Safety of the Agenda: Problem Definition An important set of results in the literature on JA are possibility theorems, sometimes called “characterisation results” =-=[11, 9]-=-. Given some axioms as desiderata for the aggregation procedure (always including consistency), such a Axioms FΦ[WR,A,S,MI ] FΦ[WR,A,N,MN ] FΦ[WR,A,S] FΦ[WR,A,N] FΦ[WR,A,I] FΦ[A,S,M I ] Representation... |

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Citation Context ...stency of a class of aggregators depending on the agenda. The following are the most important axioms for JA discussed in the literature [8, 9]: 1 This property is called weak consistency by Dietrich =-=[3]-=-, and consistency by List and Pettit [8]. Our choice of terminology is intended to stress the fact that it is a purely syntactic notion, not involving any model-theoretic concept. 2 Following List and... |

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Judgment aggregation by quota rules: Majority voting generalized
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Citation Context ...al aggregation procedure satisfying (A) and (S). A further important property is monotonicity. We introduce two different axioms for monotonicity. The first is the one commonly used in the literature =-=[4, 9]-=-. It implicitly relies on the independence axiom. The second, which to the best of our knowledge has not been formulated before, is designed to be applied to neutral procedures. For systematic procedu... |

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Citation Context ... a given type of median property, providing us with a decision procedure for the SoA problem. Work on QBF solvers has seen a lot of progress in recent years (see, e.g., the annual QBFEVAL competition =-=[10]-=-). Furthermore, understanding how a naturally arising question in judgment aggregation relates to a difficult but well-studied algorithmic problem such as QSAT2 is interesting and worthwhile in its ow... |

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Belief merging and the discursive dilemma
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Citation Context ...s to be extracted from these diverse views. Indeed, in AI, the related problem of belief merging [6] has been studied for some time, and there are interesting parallels between that literature and JA =-=[13]-=-. Given the relevance of JA to MAS, it is important to understand its computational aspects. However, to date, these have only received little attention in the literature. This can of course be explai... |