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On the construction of high dimensional simple games

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hdl:2117/97663

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Olsen, Martin
Kurz, Sascha
Molinero Albareda, XavierMés informacióMés informacióMés informació
Document typeConference report
Defense date2016
PublisherIOS Press
Rights accessOpen Access
Attribution-NonCommercial 3.0 Spain
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
ProjectASPECTOS MATEMATICOS, COMPUTACIONALES Y SOCIALES EN CONTEXTOS DE VOTACION Y DE COOPERACION. (MINECO-MTM2015-66818-P)
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. 
URIhttp://hdl.handle.net/2117/97663
ISBN978-1-61499-672-9
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  • Departament de Matemàtiques - Ponències/Comunicacions de congressos [1.139]
  • GRTJ - Grup de Recerca en Teoria de Jocs - Ponències/Comunicacions de congressos [20]
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