Bibliografische Daten exportieren
Literatur vom gleichen Autor
im Publikationsserver

# On the Construction of High Dimensional Simple Games

## Titelangaben

Olsen, Martin ; Kurz, Sascha ; Molinero, Xavier:
On the Construction of High Dimensional Simple Games.
Bayreuth , 2016 . - 13 S.

Dies ist die aktuelle Version des Eintrags.

## 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 $\chi\colon\{0,1\}^n\rightarrow \{0,1\}$. However, its naive encoding needs $2^n$ 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 $\chi$ as an intersection of $k$ threshold functions. Taylor and Zwicker have constructed a sequence of examples requiring $k\ge 2^{\frac{n}{2}-1}$ and provided a construction guaranteeing $k\le {n\choose {\lfloor n/2\rfloor}}\in 2^{n-o(n)}$. 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 for $k$ for a subclass of voting systems. As an application, we give a construction for $k\ge 2^{n-o(n)}$, i.e., there is no gain from a representation complexity point of view.

## Weitere Angaben

Publikationsform: Preprint, Postprint, Working paper, Diskussionspapier simple games; weighted games; dimension; coding theory; Hamming distance Mathematics Subject Classification Code: 91B12 (91A12 68P30) 000 Informatik,Informationswissenschaft, allgemeine Werke > 004 Informatik300 Sozialwissenschaften > 320 Politikwissenschaft500 Naturwissenschaften und Mathematik > 510 Mathematik Fakultäten > Fakultät für Mathematik, Physik und InformatikFakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches InstitutFakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut > Lehrstuhl WirtschaftsmathematikProfilfelder > Emerging Fields > Governance and ResponsibilityFakultätenProfilfelderProfilfelder > Emerging Fields Englisch Ja 18 Jul 2016 07:30 18 Jul 2016 07:30 https://epub.uni-bayreuth.de/id/eprint/2935