On the construction of high dimensional simple games

View/Open
Cita com:
hdl:2117/97663
Document typeConference report
Defense date2016
PublisherIOS Press
Rights accessOpen Access
This work is protected by the corresponding intellectual and industrial property rights.
Except where otherwise noted, its contents are licensed under a Creative Commons license
:
Attribution-NonCommercial 3.0 Spain
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 : f0; 1gn ! f0; 1g.
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 as an intersection of k
threshold functions. Taylor and Zwicker have constructed a sequence
of examples requiring k 2 n2 ¿1 and provided a construction guaranteeingk ¿ n bn=2c 2 2n¿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 k for a subclass of voting systems. As an application, we give a construction for k 2n¿o(n), i.e., there is no gain from a representation complexity point of view.
CitationOlsen, M., Kurz, S., Molinero, X. On the construction of high dimensional simple games. A: European Conference on Artificial Intelligence. "ECAI 2016: 22nd European Conference on Artificial Intelligence: 29 August–2 September 2016, The Hague, The Netherlands: proceedings". New York: IOS Press, 2016, p. 880-885.
ISBN978-1-61499-672-9
Files | Description | Size | Format | View |
---|---|---|---|---|
ECAI16_MO_SK_XM_rev3.pdf | 244,8Kb | View/Open |