Dimension of simple games and coding theory

Title data

Kurz, Sascha ; Molinero, Xavier ; Napel, Stefan ; Olsen, Martin ; Serna, Maria:
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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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.