{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,11]],"date-time":"2026-05-11T10:28:54Z","timestamp":1778495334255,"version":"3.51.4"},"reference-count":56,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2019,8,9]],"date-time":"2019-08-09T00:00:00Z","timestamp":1565308800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,8,9]],"date-time":"2019-08-09T00:00:00Z","timestamp":1565308800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Soc Choice Welf"],"published-print":{"date-parts":[[2020,1]]},"DOI":"10.1007\/s00355-019-01208-3","type":"journal-article","created":{"date-parts":[[2019,8,9]],"date-time":"2019-08-09T10:02:59Z","timestamp":1565344979000},"page":"1-45","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["The expanding approvals rule: improving proportional representation and monotonicity"],"prefix":"10.1007","volume":"54","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9757-4956","authenticated-orcid":false,"given":"Haris","family":"Aziz","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0109-7356","authenticated-orcid":false,"given":"Barton E.","family":"Lee","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2019,8,9]]},"reference":[{"key":"1208_CR1","volume-title":"Proportional representation by the single transferable vote: the system and its methods","author":"KVK Aiyar","year":"1930","unstructured":"Aiyar KVK (1930) Proportional representation by the single transferable vote: the system and its methods. The Madras Law Journal Press, Chennai"},{"key":"1208_CR2","doi-asserted-by":"publisher","first-page":"328","DOI":"10.1086\/256963","volume":"58","author":"KJ Arrow","year":"1959","unstructured":"Arrow KJ (1959) A difficulty in the concept of social welfare. J Political Econ 58:328\u2013346","journal-title":"J Political Econ"},{"issue":"13","key":"1208_CR3","doi-asserted-by":"publisher","first-page":"771","DOI":"10.1007\/s00355-011-0642-2","volume":"40","author":"F Aleskerov","year":"2013","unstructured":"Aleskerov F, Karpov A (2013) A new single transferable vote method and its axiomatic justification. Soc Choice Welf 40(13):771\u2013786","journal-title":"Soc Choice Welf"},{"key":"1208_CR4","unstructured":"Aziz H, Huang S (2016) Computational complexity of testing proportional justified representation. Technical report. arXiv:1612.06476"},{"key":"1208_CR5","unstructured":"Aziz H, Gaspers S, Gudmundsson J, Mackenzie S, Mattei N, Walsh T (2015) Computational aspects of multi-winner approval voting. In: Proceedings of the 14th international joint conference on autonomous agents and multi-agent systems (AAMAS). pp 107\u2013115"},{"key":"1208_CR6","doi-asserted-by":"publisher","first-page":"461","DOI":"10.1007\/s00355-016-1019-3","volume":"48","author":"H Aziz","year":"2017","unstructured":"Aziz H, Brill M, Conitzer V, Elkind E, Freeman R, Walsh T (2017a) Justified representation in approval-based committee voting. Soc Choice Welf 48:461\u2013485","journal-title":"Soc Choice Welf"},{"key":"1208_CR7","doi-asserted-by":"crossref","unstructured":"Aziz H, Elkind E, Faliszewski P, Lackner M, Skowron P (2017b) The Condorcet principle for multiwinner elections: from shortlisting to proportionality. In: Proceedings of the 26th international joint conference on artificial intelligence (IJCAI). pp 84\u201390","DOI":"10.24963\/ijcai.2017\/13"},{"key":"1208_CR8","doi-asserted-by":"crossref","unstructured":"Aziz H, Elkind E, Huang S, Lackner M, S\u00e1nchez-Fern\u00e1ndez L, Skowron P (2018a) On the complexity of Extended and Proportional Justified Representation. In: Proceedings of the 32nd AAAI conference on artificial intelligence (AAAI). AAAI Press, pp 902\u2013909","DOI":"10.1609\/aaai.v32i1.11478"},{"key":"1208_CR9","unstructured":"Aziz H, Lee BE, Talmon N (2018b) Proportionally representative participatory budgeting: axioms and algorithms. In: Proceedings of the 17th international joint conference on autonomous agents and multi-agent systems (AAMAS). pp 23\u201331"},{"key":"1208_CR10","volume-title":"The theory of committees and elections","author":"D Black","year":"1958","unstructured":"Black D (1958) The theory of committees and elections. Cambridge University Press, Cambridge"},{"key":"1208_CR11","unstructured":"Bowler S, Grofman B (2000) Introduction: STV as an embedded Institution. In: Elections in Australia, Ireland, and Malta under the single transferable vote: reflections on an embedded institution. pp 1\u201314"},{"issue":"1","key":"1208_CR12","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1007\/s00355-007-0268-6","volume":"31","author":"S Barber\u00e0","year":"2008","unstructured":"Barber\u00e0 S, Coelho D (2008) How to choose a non-controversial list with k names. Soc Choice Welf 31(1):79\u201396","journal-title":"Soc Choice Welf"},{"key":"1208_CR13","doi-asserted-by":"crossref","unstructured":"Brams S, Sanver R (2009) Voting systems that combine approval and preference. In: The mathematics of preference, choice and order. Springer, pp 215\u2013237","DOI":"10.1007\/978-3-540-79128-7_12"},{"key":"1208_CR14","doi-asserted-by":"crossref","unstructured":"Brill M, Freeman R, Janson S, Lackner M (2017) Phragm\u00e9n\u2019s voting methods and justified representation. In: Proceedings of the 31st AAAI conference on artificial intelligence (AAAI). AAAI Press, pp 406\u2013413","DOI":"10.1609\/aaai.v31i1.10598"},{"issue":"1","key":"1208_CR15","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1630\/095624704323026133","volume":"16","author":"Y Cabannes","year":"2004","unstructured":"Cabannes Y (2004) Participatory budgeting: a significant contribution to participatory democracy. Environ Urban 16(1):27\u201346","journal-title":"Environ Urban"},{"issue":"3","key":"1208_CR16","doi-asserted-by":"publisher","first-page":"718","DOI":"10.2307\/1957270","volume":"77","author":"JR Chamberlin","year":"1983","unstructured":"Chamberlin JR, Courant PN (1983) Representative deliberations and representative decisions: proportional representation and the Borda rule. Am Political Sci Rev 77(3):718\u2013733","journal-title":"Am Political Sci Rev"},{"key":"1208_CR17","unstructured":"Conitzer V, Rognlie M, Xia L (2009) Preference functions that score rankings and maximum likelihood estimation. In: Proceedings of the 21st international joint conference on artificial intelligence (IJCAI). AAAI Press, pp 109\u2013115"},{"key":"1208_CR18","volume-title":"Voting procedures","author":"M Dummett","year":"1984","unstructured":"Dummett M (1984) Voting procedures. Oxford University Press, Oxford"},{"key":"1208_CR19","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1016\/0165-4896(93)90012-8","volume":"26","author":"B Debord","year":"1993","unstructured":"Debord B (1993) Prudent k-choice functions: properties and algorithms. Math Soc Sci 26:63\u201377","journal-title":"Math Soc Sci"},{"key":"1208_CR20","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198292470.001.0001","volume-title":"Principles of electoral reform","author":"M Dummett","year":"1997","unstructured":"Dummett M (1997) Principles of electoral reform. Oxford University Press, Oxford"},{"issue":"2","key":"1208_CR21","doi-asserted-by":"publisher","first-page":"303","DOI":"10.2307\/2110496","volume":"21","author":"G Doron","year":"1977","unstructured":"Doron G, Kronick R (1977) Single transferrable vote: an example of a perverse social choice function. Am J Political Sci 21(2):303\u2013311","journal-title":"Am J Political Sci"},{"issue":"3","key":"1208_CR22","doi-asserted-by":"publisher","first-page":"599","DOI":"10.1007\/s00355-017-1026-z","volume":"48","author":"E Elkind","year":"2017","unstructured":"Elkind E, Faliszewski P, Skowron P, Slinko A (2017) Properties of multiwinner voting rules. Soc Choice Welf 48(3):599\u2013632","journal-title":"Soc Choice Welf"},{"key":"1208_CR23","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1016\/0166-218X(82)90070-1","volume":"4","author":"PC Fishburn","year":"1982","unstructured":"Fishburn PC (1982) Monotonicity paradoxes in the theory of elections. Discrete Appl Math 4:119\u2013134","journal-title":"Discrete Appl Math"},{"key":"1208_CR24","doi-asserted-by":"crossref","unstructured":"Faliszewski P, Talmon N (2019) A framework for approval-based budgeting methods. In: Proceedings of the 33rd AAAI conference on artificial intelligence (AAAI)","DOI":"10.1609\/aaai.v33i01.33012181"},{"key":"1208_CR25","unstructured":"Faliszewski P, Skowron P, Slinko A, Talmon N (2017) Multiwinner voting: a new challenge for social choice theory. In: Endriss U (ed) Trends in computational social choice, chapter\u00a02"},{"key":"1208_CR26","doi-asserted-by":"crossref","unstructured":"Fluschnik T, Skowron P, Triphaus M, Wilker K (2019) Fair knapsack. In: Proceedings of the 33rd AAAI conference on artificial intelligence (AAAI)","DOI":"10.1609\/aaai.v33i01.33011941"},{"issue":"3","key":"1208_CR27","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1016\/0165-4896(85)90043-5","volume":"10","author":"WV Gehrlein","year":"1985","unstructured":"Gehrlein WV (1985) The Condorcet criterion and committee selection. Math Soc Sci 10(3):199\u2013209","journal-title":"Math Soc Sci"},{"key":"1208_CR28","unstructured":"Geller C (2002) Single transferable vote with Borda elimination: a new vote-counting system. Technical report 2201, Deakin University, Faculty of Business and Law"},{"issue":"2","key":"1208_CR29","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/3340230","volume":"7","author":"Ashish Goel","year":"2019","unstructured":"Goel A, Anilesh KK, Sakshuwong S, Aitamurto T (2019) Knapsack voting for participatory budgeting. ACM Trans Econ Comput (TEAC) 7(2):8:1\u20138:27","journal-title":"ACM Transactions on Economics and Computation"},{"key":"1208_CR30","unstructured":"Hill ID (2001) Difficulties with equality of preference. Voting Matters 13"},{"key":"1208_CR31","unstructured":"Janson S (2016) Phragm\u00e9n\u2019s and Thiele\u2019s election methods. Technical report. arXiv:1611.08826 [math.HO]"},{"key":"1208_CR32","doi-asserted-by":"crossref","unstructured":"Kilgour DM (2010) Approval balloting for multi-winner elections. In: Handbook on approval voting, chapter\u00a06. Springer","DOI":"10.1007\/978-3-642-02839-7_6"},{"key":"1208_CR33","doi-asserted-by":"crossref","unstructured":"Lackner M, Skowron P (2018) Approval-based multi-winner rules and strategic voting. In: Proceedings of the 27th international joint conference on artificial intelligence (IJCAI)","DOI":"10.24963\/ijcai.2018\/47"},{"key":"1208_CR34","volume-title":"Handbook on approval voting. Studies in choice and welfare","year":"2010","unstructured":"Laslier J-F, Sanver MR (eds) (2010) Handbook on approval voting. Studies in choice and welfare. Springer, Berlin"},{"key":"1208_CR35","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1016\/0022-0531(88)90253-0","volume":"45","author":"H Moulin","year":"1988","unstructured":"Moulin H (1988) Condorcet\u2019s principle implies the No Show Paradox. J Econ Theory 45:53\u201364","journal-title":"J Econ Theory"},{"key":"1208_CR36","unstructured":"Meek BL (1994) A new approach to the single transferable vote, paper ii. Voting Matters 1"},{"issue":"4","key":"1208_CR37","doi-asserted-by":"publisher","first-page":"925","DOI":"10.2307\/2082518","volume":"89","author":"BL Monroe","year":"1995","unstructured":"Monroe BL (1995) Fully proportional representation. Am Political Sci Rev 89(4):925\u2013940","journal-title":"Am Political Sci Rev"},{"key":"1208_CR38","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-03856-8","volume-title":"Proportional representation: apportionment methods and their applications","author":"F Pukelsheim","year":"2014","unstructured":"Pukelsheim F (2014) Proportional representation: apportionment methods and their applications. Springer, Berlin"},{"key":"1208_CR39","doi-asserted-by":"publisher","first-page":"353","DOI":"10.1007\/s00355-007-0235-2","volume":"30","author":"AD Procaccia","year":"2008","unstructured":"Procaccia AD, Rosenschein JS, Zohar A (2008) On the complexity of achieving proportional representation. Soc Choice Welf 30:353\u2013362","journal-title":"Soc Choice Welf"},{"key":"1208_CR40","doi-asserted-by":"publisher","first-page":"268","DOI":"10.1007\/978-3-540-32257-3_25","volume-title":"E-Government: Towards Electronic Democracy","author":"J. Rios","year":"2005","unstructured":"Rios J, Insua DR, Fernandez E, Rivero JA (2005) Participatory budget formation through the web. In: Proceedings of E-Government: towards electronic democracy, international conference, TCGOV 2005, Bolzano, Italy, March 2-4, 2005. pp 268\u2013276"},{"issue":"6","key":"1208_CR41","doi-asserted-by":"publisher","first-page":"1027","DOI":"10.2307\/1914033","volume":"41","author":"JH Smith","year":"1973","unstructured":"Smith JH (1973) Aggregation of preferences with variable electorate. Econometrica 41(6):1027\u20131041","journal-title":"Econometrica"},{"key":"1208_CR42","unstructured":"Schulze M (2002) On Dummett\u2019s \u2018Quota Borda System\u2019. Voting Matters 15(3)"},{"key":"1208_CR43","unstructured":"Schulze M (2011) Free riding and vote management under proportional representation by single transferable vote"},{"key":"1208_CR44","doi-asserted-by":"publisher","first-page":"553","DOI":"10.1007\/s00182-009-0170-9","volume":"38","author":"MR Sanver","year":"2009","unstructured":"Sanver MR, Zwicker WS (2009) One-way monotonicity as a form of strategy-proofness. Int J Game Theory 38:553\u2013574","journal-title":"Int J Game Theory"},{"key":"1208_CR45","doi-asserted-by":"publisher","first-page":"371","DOI":"10.1007\/s00355-012-0654-6","volume":"39","author":"MR Sanver","year":"2012","unstructured":"Sanver MR, Zwicker WS (2012) Monotonicity properties and their adaptation to irresolute social choice rules. Soc Choice Welf 39:371\u2013398","journal-title":"Soc Choice Welf"},{"key":"1208_CR46","unstructured":"S\u00e1nchez-Fern\u00e1ndez L, Fisteus JA (2019) Monotonicity axioms in approval-based multi-winner voting rules. In: Proceedings of the 18th international joint conference on autonomous agents and multi-agent systems (AAMAS)"},{"key":"1208_CR47","unstructured":"S\u00e1nchez-Fern\u00e1ndez L, Fern\u00e1ndez N, Fisteus LA (2016) Fully open extensions to the D\u2019Hondt method. Technical report. arXiv:1609.05370 [cs.GT]"},{"key":"1208_CR48","unstructured":"S\u00e1nchez-Fern\u00e1ndez L, Elkind E, Lackner M (2017a) Committees providing EJR can be computed efficiently. Technical report. arXiv:1704.00356"},{"key":"1208_CR49","doi-asserted-by":"crossref","unstructured":"S\u00e1nchez-Fern\u00e1ndez L, Elkind E, Lackner M, Fern\u00e1ndez N, Fisteus JA, Basanta Val P, Skowron P (2017b) Proportional justified representation. In: Proceedings of the 31st AAAI conference on artificial intelligence (AAAI). AAAI Press","DOI":"10.1609\/aaai.v31i1.10611"},{"issue":"1","key":"1208_CR50","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1257\/jep.9.1.27","volume":"9","author":"N Tideman","year":"1995","unstructured":"Tideman N (1995) The single transferable vote. J Econ Perspect 9(1):27\u201338","journal-title":"J Econ Perspect"},{"key":"1208_CR51","volume-title":"Collective decisions and voting: the potential for public choice","author":"TN Tideman","year":"2006","unstructured":"Tideman TN (2006) Collective decisions and voting: the potential for public choice. Ashgate, Farnham"},{"key":"1208_CR52","unstructured":"The Telegraph (2011) Professor Sir Michael Dummett. http:\/\/www.telegraph.co.uk\/news\/obituaries\/culture-obituaries\/8981654\/Professor-Sir-Michael-Dummett.html"},{"issue":"1\u20132","key":"1208_CR53","doi-asserted-by":"publisher","first-page":"13","DOI":"10.1023\/A:1005082925477","volume":"103","author":"N Tideman","year":"2000","unstructured":"Tideman N, Richardson D (2000) Better voting methods through technology: the refinement-manageability trade-off in the single transferable vote. Public Choice 103(1\u20132):13\u201334","journal-title":"Public Choice"},{"key":"1208_CR54","unstructured":"Woodall DR (1994) Properties of preferential election rules. Voting Matters 3"},{"issue":"1","key":"1208_CR55","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1016\/S0166-218X(96)00100-X","volume":"77","author":"DR Woodall","year":"1997","unstructured":"Woodall DR (1997) Monotonicity of single-seat preferential election rules. Discrete Appl Math 77(1):81\u201398","journal-title":"Discrete Appl Math"},{"key":"1208_CR56","volume-title":"Handbook of computational social choice, chapter 2","author":"WS Zwicker","year":"2016","unstructured":"Zwicker WS (2016) Introduction to the theory of voting. In: Brandt F, Conitzer V, Endriss U, Lang J, Procaccia AD (eds) Handbook of computational social choice, chapter 2. Cambridge University Press, Cambridge"}],"container-title":["Social Choice and Welfare"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00355-019-01208-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00355-019-01208-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00355-019-01208-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,21]],"date-time":"2024-07-21T21:27:37Z","timestamp":1721597257000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00355-019-01208-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,8,9]]},"references-count":56,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2020,1]]}},"alternative-id":["1208"],"URL":"https:\/\/doi.org\/10.1007\/s00355-019-01208-3","relation":{},"ISSN":["0176-1714","1432-217X"],"issn-type":[{"value":"0176-1714","type":"print"},{"value":"1432-217X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,8,9]]},"assertion":[{"value":"16 September 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 July 2019","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 August 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}