{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T14:40:43Z","timestamp":1777560043396,"version":"3.51.4"},"reference-count":33,"publisher":"SAGE Publications","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["AIC"],"published-print":{"date-parts":[[2024,6,19]]},"abstract":"<jats:p>In this work, we explore the links between the Borda voting rule and belief merging operators. More precisely, we define two families of merging operators inspired by the definition of the Borda voting rule. We also introduce a notion of cancellation in belief merging, inspired by the axiomatization of the Borda voting rule proposed by Young. This allows us to provide a characterization of the drastic merging operator and of a family of merging operators defined in a way which is similar to the Borda rule.<\/jats:p>","DOI":"10.3233\/aic-220306","type":"journal-article","created":{"date-parts":[[2023,11,17]],"date-time":"2023-11-17T11:22:36Z","timestamp":1700220156000},"page":"357-375","source":"Crossref","is-referenced-by-count":1,"title":["On the links between belief merging, the Borda voting method, and the cancellation property1"],"prefix":"10.1177","volume":"37","author":[{"given":"Patricia","family":"Everaere","sequence":"first","affiliation":[{"name":"CRIStAL, UMR 9189, Univ. Lille, CNRS, Centrale Lille, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chouaib","family":"Fellah","sequence":"additional","affiliation":[{"name":"CRIL \u2013 CNRS, Universit\u00e9 d\u2019Artois, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"S\u00e9bastien","family":"Konieczny","sequence":"additional","affiliation":[{"name":"CRIL \u2013 CNRS, Universit\u00e9 d\u2019Artois, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ram\u00f3n","family":"Pino P\u00e9rez","sequence":"additional","affiliation":[{"name":"CRIL \u2013 CNRS, Universit\u00e9 d\u2019Artois, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","reference":[{"key":"10.3233\/AIC-220306_ref1","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1007\/s11127-012-9930-3","article-title":"Elections with partially ordered preferences","volume":"157","author":"Ackerman","year":"2013","journal-title":"Public Choice"},{"key":"10.3233\/AIC-220306_ref2","doi-asserted-by":"publisher","first-page":"510","DOI":"10.2307\/2274239","article-title":"On the logic of theory change: Partial meet contraction and revision functions","volume":"50","author":"Alchourr\u00f3n","year":"1985","journal-title":"Journal of Symbolic Logic"},{"key":"10.3233\/AIC-220306_ref3","unstructured":"K.J.\u00a0Arrow, Social Choice and Individual Values, 2nd edn, Wiley, New York, 1963."},{"key":"10.3233\/AIC-220306_ref4","unstructured":"K.J.\u00a0Arrow, A.K.\u00a0Sen and K.\u00a0Suzumura, eds, Handbook of Social Choice and Welfare, Vol.\u00a01, North-Holland, 2002."},{"key":"10.3233\/AIC-220306_ref6","doi-asserted-by":"publisher","first-page":"873","DOI":"10.1007\/s00355-013-0757-8","article-title":"Scoring rules for judgment aggregation","volume":"42","author":"Dietrich","year":"2014","journal-title":"Social Choice and Welfare"},{"issue":"2","key":"10.3233\/AIC-220306_ref7","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1007\/s00355-015-0914-3","article-title":"Aggregation of binary evaluations: A Borda-like approach","volume":"46","author":"Duddy","year":"2016","journal-title":"Soc. Choice Welf."},{"key":"10.3233\/AIC-220306_ref8","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1613\/jair.2034","article-title":"The strategy-proofness landscape of merging","volume":"28","author":"Everaere","year":"2007","journal-title":"Journal of Artificial Intelligence Research"},{"key":"10.3233\/AIC-220306_ref9","unstructured":"P.\u00a0Everaere, S.\u00a0Konieczny and P.\u00a0Marquis, The epistemic view of belief merging: Can we track the truth? in: Nineteenth European Conference on Artificial Intelligence (ECAI\u201910), 2010, pp.\u00a0621\u2013626."},{"issue":"12\u201313","key":"10.3233\/AIC-220306_ref10","doi-asserted-by":"crossref","first-page":"824","DOI":"10.1016\/j.artint.2010.05.001","article-title":"Disjunctive merging: Quota and Gmin merging operators","volume":"174","author":"Everaere","year":"2010","journal-title":"Artificial Intelligence"},{"key":"10.3233\/AIC-220306_ref11","unstructured":"P.\u00a0Everaere, S.\u00a0Konieczny and P.\u00a0Marquis, On egalitarian belief merging, in: Fourteenth International Conference on Principles of Knowledge Representation and Reasoning (KR\u201914), 2014."},{"key":"10.3233\/AIC-220306_ref12","unstructured":"P.\u00a0Everaere, S.\u00a0Konieczny and P.\u00a0Marquis, Counting votes for aggregating judgments, in: International Conference on Autonomous Agents and Multi-Agent Systems, (AAMAS\u201914), Paris, France, May 5\u20139, 2014, 2014, pp.\u00a01177\u20131184."},{"key":"10.3233\/AIC-220306_ref13","unstructured":"P.\u00a0Everaere, S.\u00a0Konieczny and P.\u00a0Marquis, Belief merging versus judgment aggregation, in: Fourteenth International Conference on Autonomous Agents and Multiagent Systems (AAMAS\u201915), 2015, pp.\u00a0999\u20131007."},{"issue":"2","key":"10.3233\/AIC-220306_ref14","doi-asserted-by":"publisher","first-page":"295","DOI":"10.1007\/s10992-011-9171-9","article-title":"AGM 25 years: Twenty-five years of research in belief change","volume":"40","author":"Ferm\u00e9","year":"2011","journal-title":"Journal of Philosophical Logic"},{"key":"10.3233\/AIC-220306_ref15","unstructured":"P.\u00a0G\u00e4rdenfors, Knowledge in Flux, MIT Press, 1988."},{"key":"10.3233\/AIC-220306_ref16","doi-asserted-by":"publisher","first-page":"263","DOI":"10.1016\/0004-3702(91)90069-V","article-title":"Propositional knowledge base revision and minimal change","volume":"52","author":"Katsuno","year":"1991","journal-title":"Artificial Intelligence"},{"key":"10.3233\/AIC-220306_ref17","doi-asserted-by":"crossref","unstructured":"J.S.\u00a0Kelly, Arrow Impossibility Theorems, Series in Economic Theory and Mathematical Economics, Academic Press, New York, 1978.","DOI":"10.1016\/B978-0-12-403350-4.50011-X"},{"key":"10.3233\/AIC-220306_ref18","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1016\/j.artint.2004.04.008","article-title":"DA2 merging operators","volume":"157","author":"Konieczny","year":"2004","journal-title":"Artificial Intelligence"},{"key":"10.3233\/AIC-220306_ref19","unstructured":"S.\u00a0Konieczny and R.\u00a0Pino P\u00e9rez, On the logic of merging, in: Sixth International Conference on Principles of Knowledge Representation and Reasoning (KR\u201998), 1998, pp.\u00a0488\u2013498."},{"issue":"5","key":"10.3233\/AIC-220306_ref20","doi-asserted-by":"publisher","first-page":"773","DOI":"10.1093\/logcom\/12.5.773","article-title":"Merging information under constraints: A logical framework","volume":"12","author":"Konieczny","year":"2002","journal-title":"Journal of Logic and Computation"},{"issue":"3","key":"10.3233\/AIC-220306_ref21","doi-asserted-by":"publisher","first-page":"785","DOI":"10.1016\/j.ejor.2003.06.039","article-title":"Propositional belief base merging or how to merge beliefs\/goals coming from several sources and some links with social choice theory","volume":"160","author":"Konieczny","year":"2005","journal-title":"European Journal of Operational Research"},{"issue":"2","key":"10.3233\/AIC-220306_ref22","doi-asserted-by":"publisher","first-page":"239","DOI":"10.1007\/s10992-011-9175-5","article-title":"Logic based merging","volume":"40","author":"Konieczny","year":"2011","journal-title":"Journal of Philosophical Logic"},{"issue":"2","key":"10.3233\/AIC-220306_ref23","doi-asserted-by":"publisher","first-page":"327","DOI":"10.1007\/s00355-016-1006-8","article-title":"A partial taxonomy of judgment aggregation rules and their properties","volume":"48","author":"Lang","year":"2017","journal-title":"Social Choice and Welfare"},{"issue":"1","key":"10.3233\/AIC-220306_ref24","doi-asserted-by":"publisher","first-page":"76","DOI":"10.1109\/69.667090","article-title":"Arbitration (or how to merge knowledge bases)","volume":"10","author":"Liberatore","year":"1998","journal-title":"IEEE Transactions on Knowledge and Data Engineering"},{"issue":"1","key":"10.3233\/AIC-220306_ref25","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1142\/S0218843098000040","article-title":"Merging databases under constraints","volume":"7","author":"Lin","year":"1998","journal-title":"International Journal of Cooperative Information System"},{"key":"10.3233\/AIC-220306_ref26","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1017\/S0266267102001098","article-title":"Aggregating sets of judgments. An impossibility result","volume":"18","author":"List","year":"2002","journal-title":"Economics and Philosophy"},{"key":"10.3233\/AIC-220306_ref27","doi-asserted-by":"crossref","unstructured":"C.\u00a0List and C.\u00a0Puppe, Judgment aggregation: A survey, in: The Handbook of Rational and Social Choice, Oxford University Press, 2009.","DOI":"10.1093\/acprof:oso\/9780199290420.003.0020"},{"key":"10.3233\/AIC-220306_ref28","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.artint.2017.06.003","article-title":"Impossibility in belief merging","volume":"251","author":"Mata D\u00edaz","year":"2017","journal-title":"Artificial Intelligence"},{"key":"10.3233\/AIC-220306_ref29","first-page":"87","article-title":"The axiomatic characterizations of majority voting and scoring rules","volume":"41","author":"Merlin","year":"2003","journal-title":"Math\u00e9matiques et sciences humaines"},{"issue":"2","key":"10.3233\/AIC-220306_ref30","doi-asserted-by":"publisher","first-page":"285","DOI":"10.1007\/s11229-006-9063-7","article-title":"Belief merging and the discursive dilemma: An argument-based account to paradoxes of judgment aggregation","volume":"152","author":"Pigozzi","year":"2006","journal-title":"Synthese"},{"key":"10.3233\/AIC-220306_ref31","unstructured":"G.\u00a0Pigozzi, Belief merging and judgment aggregation, in: The Stanford Encyclopedia of Philosophy (Spring 2021 Edition), E.N.\u00a0Zalta, ed., 2021, https:\/\/plato.stanford.edu\/archives\/spr2021\/entries\/belief-merging\/."},{"issue":"2","key":"10.3233\/AIC-220306_ref32","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1142\/S0218196797000095","article-title":"On the semantics of arbitration","volume":"7","author":"Revesz","year":"1997","journal-title":"International Journal of Algebra and Computation"},{"key":"10.3233\/AIC-220306_ref33","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1016\/j.jmateco.2020.11.001","article-title":"The Borda class: An axiomatic study of the Borda rule on top-truncated preferences","volume":"92","author":"Terzopoulou","year":"2021","journal-title":"Journal of Mathematical Economics"},{"key":"10.3233\/AIC-220306_ref34","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1016\/0022-0531(74)90073-8","article-title":"An axiomatization of Borda\u2019s rule","volume":"9","author":"Young","year":"1974","journal-title":"Journal of Economic Theory"}],"container-title":["AI Communications"],"original-title":[],"link":[{"URL":"https:\/\/content.iospress.com\/download?id=10.3233\/AIC-220306","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T18:28:14Z","timestamp":1777400894000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.medra.org\/servlet\/aliasResolver?alias=iospress&doi=10.3233\/AIC-220306"}},"subtitle":[],"editor":[{"given":"Zied","family":"Bouraoui","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]},{"given":"Ana\u00eblle","family":"Wilczynski","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2024,6,19]]},"references-count":33,"journal-issue":{"issue":"3"},"URL":"https:\/\/doi.org\/10.3233\/aic-220306","relation":{},"ISSN":["1875-8452","0921-7126"],"issn-type":[{"value":"1875-8452","type":"electronic"},{"value":"0921-7126","type":"print"}],"subject":[],"published":{"date-parts":[[2024,6,19]]}}}