{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,22]],"date-time":"2025-10-22T23:37:27Z","timestamp":1761176247805,"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>Apportionment methods allocate a fixed number of seats in a parliament to parties based on their vote counts. In many countries, parliamentary elections are organized by first holding separate elections in several districts and then putting the single results together. We call such elections multidistrict apportionment elections. Moreover, many countries have an additional general electoral threshold, i.e., a minimum number of votes a party must receive to win any seats in a parliament. For such methods, we study the complexity of bribery problems where an external agent seeks to increase the number of seats for a distinguished party by bribing voters within a given budget. Specifically, we investigate how adding either a general electoral threshold, or district limits for the budget, or both influences the complexity of bribery. District limits\u2014which the external agent must adhere to while still respecting the overall budget\u2014denote a maximum budget for each district, each to be spent for changing the votes only in that district. We show that adding a general electoral threshold, with or without district limits, makes the problems NP-complete for the largest-remainder method and all divisor sequence methods (including the prominent D\u2019Hondt and Sainte-Lagu\u00eb apportionment methods). We also study parameterized complexity and domain restrictions of these problems.<\/jats:p>","DOI":"10.3233\/faia251236","type":"book-chapter","created":{"date-parts":[[2025,10,22]],"date-time":"2025-10-22T09:55:27Z","timestamp":1761126927000},"source":"Crossref","is-referenced-by-count":0,"title":["District-Limited Bribery in Multidistrict Apportionment Elections with Threshold"],"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"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2604-264X","authenticated-orcid":false,"given":"Tessa","family":"Seeger","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\/FAIA251236","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,22]],"date-time":"2025-10-22T09:55:28Z","timestamp":1761126928000},"score":1,"resource":{"primary":{"URL":"https:\/\/ebooks.iospress.nl\/doi\/10.3233\/FAIA251236"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,21]]},"ISBN":["9781643686318"],"references-count":0,"URL":"https:\/\/doi.org\/10.3233\/faia251236","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]]}}}