## Title data

Kurz, Sascha ; Molinero, Xavier ; Olsen, Martin:

**On the Construction of High Dimensional Simple Games.**

2016

*Event:* 22. European Conference on Artificial Intelligence (ECAI) 2016
, 29.08-02.09.2016
, The Hague, Holland.

(Conference item: Conference
,
Speech
)

## Related URLs

## Abstract in another language

Voting is a commonly applied method for the aggregation of the preferences of multiple agents into a joint decision. If preferences are binary, i.e., yes and no, every voting system can be described by a (monotone) Boolean function. However, its naive encoding needs 2n bits. The subclass of threshold functions, which is sufficient for homogeneous agents, allows a more succinct representation using n weights and one threshold. For heterogeneous agents, one can represent χ as an intersection of k threshold functions. Taylor and Zwicker have constructed a sequence of examples requiring k>=2^(n/2-1). The magnitude of the worst-case situation was thought to be determined by Elkind et al. in 2008, but the analysis unfortunately turned out to be wrong. Here we uncover a relation to coding theory that allows the determination of the minimum number k for a subclass of voting systems. As an application, we give a new construction closing the gap from a representation complexity point of view.

## Further data

Item Type: | Conference item (Speech) |
---|---|

Refereed: | Yes |

Additional notes: | speaker: Martin Olsen |

Keywords: | simple games; dimension; error-correcting codes |

Subject classification: | Mathematics Subject Classification Code: 91B12 91A12 68P30 |

Institutions of the University: | Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics in Economy Profile Fields > Emerging Fields Profile Fields > Emerging Fields > Governance and Responsibility Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Profile Fields |

Result of work at the UBT: | Yes |

DDC Subjects: | 000 Computer Science, information, general works > 004 Computer science 500 Science > 510 Mathematics |

Date Deposited: | 22 Nov 2016 09:36 |

Last Modified: | 23 Nov 2016 06:57 |

URI: | https://eref.uni-bayreuth.de/id/eprint/35166 |