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Dimension of simple games and coding theory

Title data

Kurz, Sascha ; Molinero, Xavier ; Napel, Stefan ; Olsen, Martin ; Serna, Matia:
Dimension of simple games and coding theory.
2018
Event: European Meeting on Game Theory 2018 : Sing14 , 16.-18.07.2018 , Bayreuth.
(Conference item: Conference , Speech )

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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 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 the game as an intersection of k threshold functions. Here we uncover a relation to coding theory that allows the determination of the minimum number for k, called the dimension, for a subclass of voting systems.

Further data

Item Type: Conference item (Speech)
Refereed: No
Additional notes: Speaker: Sascha Kurz
Keywords: simple games; weighted games; dimension; coding theory; Hamming distance
Subject classification: Mathematics Subject Classification Code: 91B12 (91A12 68P30)
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics in Economy
Faculties > Faculty of Law, Business and Economics > Department of Economics > Chair Economics IV > Chair Economics IV - Univ.-Prof. Dr. Stefan Napel
Profile Fields > Emerging Fields > Governance and Responsibility
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Law, Business and Economics
Faculties > Faculty of Law, Business and Economics > Department of Economics
Faculties > Faculty of Law, Business and Economics > Department of Economics > Chair Economics IV
Profile Fields
Profile Fields > Emerging Fields
Result of work at the UBT: Yes
DDC Subjects: 000 Computer Science, information, general works > 004 Computer science
300 Social sciences > 320 Political science
500 Science > 510 Mathematics
Date Deposited: 16 Jul 2018 07:36
Last Modified: 16 Jul 2018 07:36
URI: https://eref.uni-bayreuth.de/id/eprint/45079