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On the Construction of High Dimensional Simple Games

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Kurz, Sascha ; Molinero, Xavier ; Olsen, Martin:
On the Construction of High Dimensional Simple Games.
2016
Veranstaltung: 22. European Conference on Artificial Intelligence (ECAI) 2016 , 29.08-02.09.2016 , The Hague, Holland.
(Veranstaltungsbeitrag: Kongress/Konferenz/Symposium/Tagung , Vortrag )

Abstract

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.

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Publikationsform: Veranstaltungsbeitrag (Vortrag)
Begutachteter Beitrag: Ja
Zusätzliche Informationen: speaker: Martin Olsen
Keywords: simple games; dimension; error-correcting codes
Fachklassifikationen: Mathematics Subject Classification Code: 91B12 91A12 68P30
Institutionen der Universität: Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut
Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut > Lehrstuhl Wirtschaftsmathematik
Profilfelder > Emerging Fields
Profilfelder > Emerging Fields > Governance and Responsibility
Fakultäten
Fakultäten > Fakultät für Mathematik, Physik und Informatik
Profilfelder
Titel an der UBT entstanden: Ja
Themengebiete aus DDC: 000 Informatik,Informationswissenschaft, allgemeine Werke > 004 Informatik
500 Naturwissenschaften und Mathematik > 510 Mathematik
Eingestellt am: 22 Nov 2016 09:36
Letzte Änderung: 23 Nov 2016 06:57
URI: https://eref.uni-bayreuth.de/id/eprint/35166