{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,22]],"date-time":"2025-02-22T05:26:31Z","timestamp":1740201991917,"version":"3.37.3"},"reference-count":0,"publisher":"IOS Press","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2016]]},"abstract":"<jats:p>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., &amp;ldquo;yes&amp;rdquo; and &amp;ldquo;no&amp;rdquo;, every voting system can be described by a (monotone) Boolean function &amp;chi;:{0,1}n&amp;rarr;{0,1}. However, its naive encoding needs 2nbits. 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 &amp;chi; as an intersection of k threshold functions. Taylor and Zwicker have constructed a sequence of examples requiringand provided a construction guaranteeing. The magnitude of the worst-case situation was 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&amp;ge;2n&amp;minus;o&amp;lpar;n&amp;rpar;, i.e., there is no gain from a representation complexity point of view.<\/jats:p>","DOI":"10.3233\/978-1-61499-672-9-880","type":"book-chapter","created":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:27:05Z","timestamp":1740133625000},"source":"Crossref","is-referenced-by-count":0,"title":["On the Construction of High-Dimensional Simple Games"],"prefix":"10.3233","author":[{"family":"Olsen Martin","sequence":"additional","affiliation":[]},{"family":"Kurz Sascha","sequence":"additional","affiliation":[]},{"family":"Molinero Xavier","sequence":"additional","affiliation":[]}],"member":"7437","container-title":["Frontiers in Artificial Intelligence and Applications","ECAI 2016"],"original-title":[],"deposited":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:39:01Z","timestamp":1740134341000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.medra.org\/servlet\/aliasResolver?alias=iospressISBN&isbn=978-1-61499-671-2&spage=880&doi=10.3233\/978-1-61499-672-9-880"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016]]},"references-count":0,"URL":"https:\/\/doi.org\/10.3233\/978-1-61499-672-9-880","relation":{},"ISSN":["0922-6389"],"issn-type":[{"value":"0922-6389","type":"print"}],"subject":[],"published":{"date-parts":[[2016]]}}}