{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,22]],"date-time":"2025-10-22T23:37:30Z","timestamp":1761176250816,"version":"build-2065373602"},"reference-count":0,"publisher":"IOS Press","isbn-type":[{"value":"9781643686318","type":"electronic"}],"license":[{"start":{"date-parts":[[2025,10,21]],"date-time":"2025-10-21T00:00:00Z","timestamp":1761004800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,10,21]]},"abstract":"<jats:p>Weighted voting games are a popular class of coalitional games that are widely used to model real-life situations of decision-making. They can be applied, for instance, to analyze legislative processes in parliaments or voting in corporate structures. Various ways of tampering with these games have been studied, among them merging or splitting players, fiddling with the quota, and controlling weighted voting games by adding or deleting players. While the complexity of control by adding players to such games so as to change or maintain a given player\u2019s power has been recently settled, the complexity of control by deleting players from such games (with the same goals) remained open. We show that when the players\u2019 power is measured by the probabilistic Penrose\u2013Banzhaf index, some of these problems are complete for NPPP\u2014the class of problems solvable by NP machines equipped with a PP (\u201cprobabilistic polynomial time\u201d) oracle. Our results optimally improve the currently known lower bounds of hardness for much smaller complexity classes, thus providing protection against SAT-solving techniques in practical applications.<\/jats:p>","DOI":"10.3233\/faia251244","type":"book-chapter","created":{"date-parts":[[2025,10,22]],"date-time":"2025-10-22T09:55:44Z","timestamp":1761126944000},"source":"Crossref","is-referenced-by-count":0,"title":["Control by Deleting Players from Weighted Voting Games Is NPPP-Complete for the Penrose\u2013Banzhaf Power Index"],"prefix":"10.3233","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6652-6433","authenticated-orcid":false,"given":"Joanna","family":"Kaczmarek","sequence":"first","affiliation":[{"name":"Institut f\u00fcr Informatik, MNF, Heinrich-Heine-Universit\u00e4t D\u00fcsseldorf, D\u00fcsseldorf, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0589-3616","authenticated-orcid":false,"given":"J\u00f6rg","family":"Rothe","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Informatik, MNF, Heinrich-Heine-Universit\u00e4t D\u00fcsseldorf, D\u00fcsseldorf, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"7437","container-title":["Frontiers in Artificial Intelligence and Applications","ECAI 2025"],"original-title":[],"link":[{"URL":"https:\/\/ebooks.iospress.nl\/pdf\/doi\/10.3233\/FAIA251244","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,22]],"date-time":"2025-10-22T09:55:44Z","timestamp":1761126944000},"score":1,"resource":{"primary":{"URL":"https:\/\/ebooks.iospress.nl\/doi\/10.3233\/FAIA251244"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,21]]},"ISBN":["9781643686318"],"references-count":0,"URL":"https:\/\/doi.org\/10.3233\/faia251244","relation":{},"ISSN":["0922-6389","1879-8314"],"issn-type":[{"value":"0922-6389","type":"print"},{"value":"1879-8314","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,10,21]]}}}