### Abstract

We consider the following decision scenario: a society of voters has to find an agreement on a set of proposals, and every single proposal is to be accepted or rejected. Each voter supports a certain subset of the proposals-The favorite ballot of this voter-and opposes the remaining ones. He accepts a ballot if he supports more than half of the proposals in this ballot. The task is to decide whether there exists a ballot approving a set of selected proposals (agenda) such that all voters (or a strict majority of them) accept this ballot. On the negative side both problems are NP-complete, and on the positive side they are fixed-parameter tractable with respect to the total number of proposals or with respect to the total number of voters. We look into further natural parameters and study their influence on the computational complexity of both problems, thereby providing both tractability and intractability results. Furthermore, we provide tight combinatorial bounds on the worst-case size of an accepted ballot in terms of the number of voters.

Original language | English (US) |
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Title of host publication | Algorithmic Decision Theory - Third International Conference, ADT 2013, Proceedings |

Pages | 30-44 |

Number of pages | 15 |

DOIs | |

State | Published - Dec 16 2013 |

Externally published | Yes |

Event | 3rd International Conference on Algorithmic Decision Theory, ADT 2013 - Bruxelles, Belgium Duration: Nov 13 2013 → Nov 15 2013 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 8176 LNAI |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 3rd International Conference on Algorithmic Decision Theory, ADT 2013 |
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Country | Belgium |

City | Bruxelles |

Period | 11/13/13 → 11/15/13 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Algorithmic Decision Theory - Third International Conference, ADT 2013, Proceedings*(pp. 30-44). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8176 LNAI). https://doi.org/10.1007/978-3-642-41575-3-3