{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,10]],"date-time":"2026-02-10T01:28:38Z","timestamp":1770686918956,"version":"3.49.0"},"reference-count":47,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2020,10,16]],"date-time":"2020-10-16T00:00:00Z","timestamp":1602806400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"name":"UNSW Scientia Fellowship"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Econ. Comput."],"published-print":{"date-parts":[[2020,11,30]]},"abstract":"<jats:p>\n            We consider a setting in which agents vote to choose a fair mixture of public outcomes. The agents have dichotomous preferences: Each outcome is liked or disliked by an agent. We discuss three outstanding voting rules. The\n            <jats:italic>Conditional Utilitarian<\/jats:italic>\n            rule, a variant of the random dictator, is strategyproof and guarantees to any group of like-minded agents an influence proportional to its size. It is easier to compute and more efficient than the familiar\n            <jats:italic>Random Priority<\/jats:italic>\n            rule. We show, both formally and by numerical experiments, that its inefficiency is low when the number of agents is low. The efficient\n            <jats:italic>Egalitarian<\/jats:italic>\n            rule protects individual agents but not coalitions. It is\n            <jats:italic>excludable strategyproof<\/jats:italic>\n            : An agent does not want to lie if she cannot consume outcomes she claims to dislike. The efficient\n            <jats:italic>Max Nash Product<\/jats:italic>\n            rule offers the strongest welfare guarantees to coalitions, which can force any outcome with a probability proportional to their size. But it even fails the excludable form of strategyproofness.\n          <\/jats:p>","DOI":"10.1145\/3417738","type":"journal-article","created":{"date-parts":[[2020,10,16]],"date-time":"2020-10-16T22:24:56Z","timestamp":1602887096000},"page":"1-27","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":10,"title":["Fair Mixing"],"prefix":"10.1145","volume":"8","author":[{"given":"Haris","family":"Aziz","sequence":"first","affiliation":[{"name":"UNSW Sydney and Data61 CSIRO, UNSW Sydney, Australia, NSW"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Anna","family":"Bogomolnaia","sequence":"additional","affiliation":[{"name":"University of Glasgow and HSE St Petersburg, Glasgow, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Herv\u00e9","family":"Moulin","sequence":"additional","affiliation":[{"name":"University of Glasgow and HSE St Petersburg, Glasgow, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2020,10,16]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.2307\/2998580"},{"key":"e_1_2_1_2_1","volume-title":"Proceedings of the 28th International Joint Conference on Artificial Intelligence (IJCAI\u201919)","author":"Airiau S.","unstructured":"S. Airiau , H. Aziz , I. Caragiannis , J. Kruger , J. Lang , and D. Peters . 2019. Portioning using ordinal preferences: Fairness and efficiency . In Proceedings of the 28th International Joint Conference on Artificial Intelligence (IJCAI\u201919) . S. Airiau, H. Aziz, I. Caragiannis, J. Kruger, J. Lang, and D. Peters. 2019. Portioning using ordinal preferences: Fairness and efficiency. In Proceedings of the 28th International Joint Conference on Artificial Intelligence (IJCAI\u201919)."},{"key":"e_1_2_1_3_1","volume-title":"Proceedings of the 23rd International Joint Conference on Artificial Intelligence. AAAI Press, 34--40","author":"Aziz H.","year":"2013","unstructured":"H. Aziz . 2013 . Maximal recursive rule: A new social decision scheme . In Proceedings of the 23rd International Joint Conference on Artificial Intelligence. AAAI Press, 34--40 . H. Aziz. 2013. Maximal recursive rule: A new social decision scheme. In Proceedings of the 23rd International Joint Conference on Artificial Intelligence. AAAI Press, 34--40."},{"key":"e_1_2_1_4_1","volume-title":"The Future of Economic Design, J.-F","author":"Aziz H.","unstructured":"H. Aziz . 2019. A probabilistic approach to voting, allocation, matching, and coalition formation . In The Future of Economic Design, J.-F . Laslier, H. Moulin, R. Sanver, and W. S. Zwicker (Eds.). Springer . H. Aziz. 2019. A probabilistic approach to voting, allocation, matching, and coalition formation. In The Future of Economic Design, J.-F. Laslier, H. Moulin, R. Sanver, and W. S. Zwicker (Eds.). Springer."},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.geb.2018.03.005"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.econlet.2013.09.006"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00355-016-1019-3"},{"key":"e_1_2_1_8_1","volume-title":"Proceedings of the 32nd AAAI Conference on Artificial Intelligence (AAAI\u201918)","author":"Aziz H.","unstructured":"H. Aziz , E. Elkind , S. Huang , M. Lackner , L. S\u00e1nchez-Fern\u00e1ndez , and P. Skowron . 2018. On the complexity of extended and proportional justified representation . In Proceedings of the 32nd AAAI Conference on Artificial Intelligence (AAAI\u201918) . AAAI Press, 902--909. H. Aziz, E. Elkind, S. Huang, M. Lackner, L. S\u00e1nchez-Fern\u00e1ndez, and P. Skowron. 2018. On the complexity of extended and proportional justified representation. In Proceedings of the 32nd AAAI Conference on Artificial Intelligence (AAAI\u201918). AAAI Press, 902--909."},{"key":"e_1_2_1_9_1","volume-title":"Proceedings of the 28th AAAI Conference on Artificial Intelligence. AAAI Press, 559--565","author":"Aziz H.","unstructured":"H. Aziz and P. Stursberg . 2014. A generalization of probabilistic serial to randomized social choice . In Proceedings of the 28th AAAI Conference on Artificial Intelligence. AAAI Press, 559--565 . H. Aziz and P. Stursberg. 2014. A generalization of probabilistic serial to randomized social choice. In Proceedings of the 28th AAAI Conference on Artificial Intelligence. AAAI Press, 559--565."},{"key":"e_1_2_1_10_1","volume-title":"Proceedings of the 31st AAAI Conference on Artificial Intelligence. AAAI Press, 376--382","author":"Benade G.","unstructured":"G. Benade , S. Nath , A. D. Procaccia , and N. Shah . 2017. Preference elicitation for participatory budgeting . In Proceedings of the 31st AAAI Conference on Artificial Intelligence. AAAI Press, 376--382 . G. Benade, S. Nath, A. D. Procaccia, and N. Shah. 2017. Preference elicitation for participatory budgeting. In Proceedings of the 31st AAAI Conference on Artificial Intelligence. AAAI Press, 376--382."},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1111\/jpet.12258"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1006\/jeth.2000.2710"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1468-0262.2004.00483.x"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.3982\/ECTA14564"},{"key":"e_1_2_1_15_1","volume-title":"University of Glasgow","author":"Bogomolnaia A.","year":"2002","unstructured":"A. Bogomolnaia , H. Moulin , and R. Stong . 2002. Collective choice under dichotomous preferences. Mimeo , University of Glasgow , 2002 . A. Bogomolnaia, H. Moulin, and R. Stong. 2002. Collective choice under dichotomous preferences. Mimeo, University of Glasgow, 2002."},{"key":"e_1_2_1_16_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jet.2004.05.005"},{"key":"e_1_2_1_17_1","volume-title":"Proceedings of the 14th International Conference on Autonomous Agents and Multi-Agent Systems. IFAAMAS, 1411--1419","author":"Brandl F.","unstructured":"F. Brandl , F. Brandt , and J. Hofbauer . 2015. Incentives for participation and abstention in probabilistic social choice . In Proceedings of the 14th International Conference on Autonomous Agents and Multi-Agent Systems. IFAAMAS, 1411--1419 . F. Brandl, F. Brandt, and J. Hofbauer. 2015. Incentives for participation and abstention in probabilistic social choice. In Proceedings of the 14th International Conference on Autonomous Agents and Multi-Agent Systems. IFAAMAS, 1411--1419."},{"key":"e_1_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.3982\/ECTA13337"},{"key":"e_1_2_1_19_1","first-page":"3","article-title":"Rolling the dice: Recent results in probabilistic social choice. In Trends in Computational Social Choice, U. Endriss (Ed.). AI Access","volume":"1","author":"Brandt F.","year":"2017","unstructured":"F. Brandt . 2017 . Rolling the dice: Recent results in probabilistic social choice. In Trends in Computational Social Choice, U. Endriss (Ed.). AI Access , Chapter 1 , 3 -- 26 . F. Brandt. 2017. Rolling the dice: Recent results in probabilistic social choice. In Trends in Computational Social Choice, U. Endriss (Ed.). AI Access, Chapter 1, 3--26.","journal-title":"Chapter"},{"key":"e_1_2_1_20_1","doi-asserted-by":"publisher","DOI":"10.1630\/095624704323026133"},{"key":"e_1_2_1_21_1","volume-title":"Proceedings of the 17th ACM Conference on Economics and Computation (EC\u201916)","author":"Caragiannis I.","unstructured":"I. Caragiannis , D. Kurokawa , H. Moulin , A. D. Procaccia , N. Shah , and J. Wang . 2016. The unreasonable fairness of maximum Nash welfare . In Proceedings of the 17th ACM Conference on Economics and Computation (EC\u201916) . 305--322. I. Caragiannis, D. Kurokawa, H. Moulin, A. D. Procaccia, N. Shah, and J. Wang. 2016. The unreasonable fairness of maximum Nash welfare. In Proceedings of the 17th ACM Conference on Economics and Computation (EC\u201916). 305--322."},{"key":"e_1_2_1_22_1","volume-title":"Solutions and Applications","author":"Driessen T.","unstructured":"T. Driessen . 1988. Cooperative Games , Solutions and Applications . Kluwer . T. Driessen. 1988. Cooperative Games, Solutions and Applications. Kluwer."},{"key":"e_1_2_1_23_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.mathsocsci.2014.10.005"},{"key":"e_1_2_1_24_1","volume-title":"Proceedings of the 12th International Conference on Web and Internet Economics (WINE\u201916)","author":"Fain B.","unstructured":"B. Fain , A. Goel , and K. Munagala . 2016. The core of the participatory budgeting problem . In Proceedings of the 12th International Conference on Web and Internet Economics (WINE\u201916) . 384--399. B. Fain, A. Goel, and K. Munagala. 2016. The core of the participatory budgeting problem. In Proceedings of the 12th International Conference on Web and Internet Economics (WINE\u201916). 384--399."},{"key":"e_1_2_1_25_1","unstructured":"P. Faliszewski P. Skowron A. Slinko and N. Talmon. 2017. Multiwinner voting: A new challenge for social choice theory. In Trends in Computational Social Choice U. Endriss (Ed.). Chapter 2.  P. Faliszewski P. Skowron A. Slinko and N. Talmon. 2017. Multiwinner voting: A new challenge for social choice theory. In Trends in Computational Social Choice U. Endriss (Ed.). Chapter 2."},{"key":"e_1_2_1_26_1","doi-asserted-by":"publisher","DOI":"10.2307\/2297786"},{"key":"e_1_2_1_27_1","doi-asserted-by":"publisher","DOI":"10.1080\/0025570X.1983.11977044"},{"key":"e_1_2_1_28_1","volume-title":"Proceedings of the 33rd AAAI Conference on Artificial Intelligence. AAAI","author":"Skowron T.","unstructured":"T. FluschnikP. Skowron , M. Triphaus and K. Wilker . 2019. Fair knapsack . In Proceedings of the 33rd AAAI Conference on Artificial Intelligence. AAAI , 1941--1948. T. FluschnikP. Skowron, M. Triphaus and K. Wilker. 2019. Fair knapsack. In Proceedings of the 33rd AAAI Conference on Artificial Intelligence. AAAI, 1941--1948."},{"key":"e_1_2_1_29_1","doi-asserted-by":"publisher","DOI":"10.2307\/1911681"},{"key":"e_1_2_1_30_1","doi-asserted-by":"publisher","DOI":"10.2307\/1123120"},{"key":"e_1_2_1_31_1","volume-title":"The Future of Economic Design","author":"Grandi U.","unstructured":"U. Grandi . 2017. Agent-mediated social choice . In The Future of Economic Design , J. F. Laslier, H. Moulin, R. Sanver, and W. Zwicker (Eds.). Springer . U. Grandi. 2017. Agent-mediated social choice. In The Future of Economic Design, J. F. Laslier, H. Moulin, R. Sanver, and W. Zwicker (Eds.). Springer."},{"key":"e_1_2_1_32_1","first-page":"35","article-title":"Monitoring the monitors: EU enlargement conditionality and minority protection in the CEECs","volume":"1","author":"Hughes J.","year":"2003","unstructured":"J. Hughes and G. Sasse . 2003 . Monitoring the monitors: EU enlargement conditionality and minority protection in the CEECs . J. Ethnopol. Minor. Iss. Eur. 1 (2003), 35 . J. Hughes and G. Sasse. 2003. Monitoring the monitors: EU enlargement conditionality and minority protection in the CEECs. J. Ethnopol. Minor. Iss. Eur. 1 (2003), 35.","journal-title":"J. Ethnopol. Minor. Iss. Eur."},{"key":"e_1_2_1_33_1","doi-asserted-by":"publisher","DOI":"10.1006\/game.1993.1010"},{"key":"e_1_2_1_34_1","volume-title":"Proceedings of the 34rd AAAI Conference on Artificial Intelligence. AAAI.","author":"Michorzewski M.","unstructured":"M. Michorzewski , D. Peters , and P. Skowron . 2020. Price of fairness in budget division and probabilistic social choice . In Proceedings of the 34rd AAAI Conference on Artificial Intelligence. AAAI. M. Michorzewski, D. Peters, and P. Skowron. 2020. Price of fairness in budget division and probabilistic social choice. In Proceedings of the 34rd AAAI Conference on Artificial Intelligence. AAAI."},{"key":"e_1_2_1_35_1","doi-asserted-by":"publisher","DOI":"10.2307\/2297154"},{"key":"e_1_2_1_36_1","doi-asserted-by":"publisher","DOI":"10.2307\/1912535"},{"key":"e_1_2_1_37_1","volume-title":"Axioms of Cooperative Decision Making","author":"Moulin H.","unstructured":"H. Moulin . 1988. Axioms of Cooperative Decision Making . Cambridge University Press , UK. H. Moulin. 1988. Axioms of Cooperative Decision Making. Cambridge University Press, UK."},{"key":"e_1_2_1_38_1","volume-title":"Fair Division and Collective Welfare","author":"Moulin H.","unstructured":"H. Moulin . 2003. Fair Division and Collective Welfare . The MIT Press, Cambridge , MA. H. Moulin. 2003. Fair Division and Collective Welfare. The MIT Press, Cambridge, MA."},{"key":"e_1_2_1_39_1","doi-asserted-by":"publisher","DOI":"10.1146\/annurev-economics-080218-025559"},{"key":"e_1_2_1_40_1","doi-asserted-by":"publisher","DOI":"10.2307\/1907266"},{"key":"e_1_2_1_41_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-405X(00)00065-9"},{"key":"e_1_2_1_42_1","doi-asserted-by":"publisher","DOI":"10.2307\/1952795"},{"key":"e_1_2_1_43_1","first-page":"101","article-title":"The problem of fair division","volume":"16","author":"Steinhaus H.","year":"1948","unstructured":"H. Steinhaus . 1948 . The problem of fair division . Econometrica 16 (1948), 101 -- 104 . H. Steinhaus. 1948. The problem of fair division. Econometrica 16 (1948), 101--104.","journal-title":"Econometrica"},{"key":"e_1_2_1_44_1","volume-title":"Handbook of Computational Social Choice","author":"Thomson W.","unstructured":"W. Thomson . 2016. Introduction to the theory of fair allocation . In Handbook of Computational Social Choice , F. Brandt, V. Conitzer, U. Endriss, J. Lang, and A. D. Procaccia (Eds.). Cambridge University Press , Chapter 11. W. Thomson. 2016. Introduction to the theory of fair allocation. In Handbook of Computational Social Choice, F. Brandt, V. Conitzer, U. Endriss, J. Lang, and A. D. Procaccia (Eds.). Cambridge University Press, Chapter 11."},{"key":"e_1_2_1_45_1","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0531(74)90075-1"},{"key":"e_1_2_1_46_1","doi-asserted-by":"publisher","DOI":"10.1137\/110832021"},{"key":"e_1_2_1_47_1","volume-title":"The case for cumulative voting. Wisc. Law Rev. 49--56","author":"Young G.","year":"1950","unstructured":"G. Young . 1950. The case for cumulative voting. Wisc. Law Rev. 49--56 ( 1950 ). G. Young. 1950. The case for cumulative voting. Wisc. Law Rev. 49--56 (1950)."}],"container-title":["ACM Transactions on Economics and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3417738","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3417738","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T22:01:14Z","timestamp":1750197674000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3417738"}},"subtitle":["The Case of Dichotomous Preferences"],"short-title":[],"issued":{"date-parts":[[2020,10,16]]},"references-count":47,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2020,11,30]]}},"alternative-id":["10.1145\/3417738"],"URL":"https:\/\/doi.org\/10.1145\/3417738","relation":{},"ISSN":["2167-8375","2167-8383"],"issn-type":[{"value":"2167-8375","type":"print"},{"value":"2167-8383","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,10,16]]},"assertion":[{"value":"2019-10-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2020-06-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2020-10-16","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}