[{"publication":"Mathematical Social Sciences","abstract":[{"text":"There are a number of school choice problems in which students are heterogeneous according to the number of seats they occupy at the school they are assigned to. We propose a weighted school choice problem by assigning each student a so-called weight and formulate the weighted top trading cycles algorithm (WTTC) to find a matching. The WTTC is strategy-proof and results in a Pareto efficient matching. While the WTTC is a robust extension of the TTC when weights are introduced, it is no longer guaranteed that each student gets a seat at a school even if the overall capacity exceeds the sum of weights. Additionally, the WTTC introduces a trade-off between weights and priorities as a student with a higher weight has a disadvantage to be matched to a particular school compared to a student with the same schools’ priorities but a smaller weight.","lang":"eng"}],"file":[{"creator":"nmaraun","date_created":"2024-10-08T11:53:39Z","date_updated":"2024-10-08T11:53:39Z","relation":"main_file","access_level":"closed","file_size":611017,"file_name":"1-s2.0-S0165489624000817-main.pdf","success":1,"content_type":"application/pdf","file_id":"56421"}],"date_created":"2024-10-08T11:52:59Z","keyword":["Matching","School choice","College admission problems","Top trading cycles","Pareto efficiency","Strategy-proofness"],"type":"journal_article","department":[{"_id":"200"}],"year":"2024","title":"Weighted school choice problems and the weighted top trading cycles mechanism","author":[{"last_name":"Stroh-Maraun","first_name":"Nadja","full_name":"Stroh-Maraun, Nadja","id":"13264"}],"publication_identifier":{"issn":["0165-4896"]},"publication_status":"published","date_updated":"2025-02-28T11:33:48Z","article_type":"original","intvolume":"       132","main_file_link":[{"url":"https://www.sciencedirect.com/science/article/pii/S0165489624000817?via%3Dihub","open_access":"1"}],"language":[{"iso":"eng"}],"doi":"10.1016/j.mathsocsci.2024.09.001","file_date_updated":"2024-10-08T11:53:39Z","citation":{"ama":"Stroh-Maraun N. Weighted school choice problems and the weighted top trading cycles mechanism. <i>Mathematical Social Sciences</i>. 2024;132:49-56. doi:<a href=\"https://doi.org/10.1016/j.mathsocsci.2024.09.001\">10.1016/j.mathsocsci.2024.09.001</a>","short":"N. Stroh-Maraun, Mathematical Social Sciences 132 (2024) 49–56.","chicago":"Stroh-Maraun, Nadja. “Weighted School Choice Problems and the Weighted Top Trading Cycles Mechanism.” <i>Mathematical Social Sciences</i> 132 (2024): 49–56. <a href=\"https://doi.org/10.1016/j.mathsocsci.2024.09.001\">https://doi.org/10.1016/j.mathsocsci.2024.09.001</a>.","bibtex":"@article{Stroh-Maraun_2024, title={Weighted school choice problems and the weighted top trading cycles mechanism}, volume={132}, DOI={<a href=\"https://doi.org/10.1016/j.mathsocsci.2024.09.001\">10.1016/j.mathsocsci.2024.09.001</a>}, journal={Mathematical Social Sciences}, publisher={Elsevier BV}, author={Stroh-Maraun, Nadja}, year={2024}, pages={49–56} }","mla":"Stroh-Maraun, Nadja. “Weighted School Choice Problems and the Weighted Top Trading Cycles Mechanism.” <i>Mathematical Social Sciences</i>, vol. 132, Elsevier BV, 2024, pp. 49–56, doi:<a href=\"https://doi.org/10.1016/j.mathsocsci.2024.09.001\">10.1016/j.mathsocsci.2024.09.001</a>.","apa":"Stroh-Maraun, N. (2024). Weighted school choice problems and the weighted top trading cycles mechanism. <i>Mathematical Social Sciences</i>, <i>132</i>, 49–56. <a href=\"https://doi.org/10.1016/j.mathsocsci.2024.09.001\">https://doi.org/10.1016/j.mathsocsci.2024.09.001</a>","ieee":"N. Stroh-Maraun, “Weighted school choice problems and the weighted top trading cycles mechanism,” <i>Mathematical Social Sciences</i>, vol. 132, pp. 49–56, 2024, doi: <a href=\"https://doi.org/10.1016/j.mathsocsci.2024.09.001\">10.1016/j.mathsocsci.2024.09.001</a>."},"project":[{"_id":"7","grant_number":"160364472","name":"SFB 901 - A3: SFB 901 - Der Markt für Services: Anreize, Algorithmen, Implementation (Teilprojekt A3)"},{"_id":"1","grant_number":"160364472","name":"SFB 901: SFB 901: On-The-Fly Computing - Individualisierte IT-Dienstleistungen in dynamischen Märkten "},{"_id":"2","name":"SFB 901 - A: SFB 901 - Projektbereich A: Algorithmische und ökonomische Grundlagen für die Organisation großer, dynamischer Märkte"}],"oa":"1","status":"public","jel":["C78","D47"],"has_accepted_license":"1","page":"49-56","funded_apc":"1","_id":"56420","publisher":"Elsevier BV","user_id":"477","ddc":["330"],"volume":132},{"file_date_updated":"2018-10-31T08:29:51Z","citation":{"apa":"Haake, C.-J. (2008). Two support results for the Kalai–Smorodinsky solution in small object division markets. <i>Mathematical Social Sciences</i>, <i>57</i>(2), 177–187. <a href=\"https://doi.org/10.1016/j.mathsocsci.2008.09.004\">https://doi.org/10.1016/j.mathsocsci.2008.09.004</a>","ieee":"C.-J. Haake, “Two support results for the Kalai–Smorodinsky solution in small object division markets,” <i>Mathematical Social Sciences</i>, vol. 57, no. 2, pp. 177–187, 2008.","chicago":"Haake, Claus-Jochen. “Two Support Results for the Kalai–Smorodinsky Solution in Small Object Division Markets.” <i>Mathematical Social Sciences</i> 57, no. 2 (2008): 177–87. <a href=\"https://doi.org/10.1016/j.mathsocsci.2008.09.004\">https://doi.org/10.1016/j.mathsocsci.2008.09.004</a>.","short":"C.-J. Haake, Mathematical Social Sciences 57 (2008) 177–187.","mla":"Haake, Claus-Jochen. “Two Support Results for the Kalai–Smorodinsky Solution in Small Object Division Markets.” <i>Mathematical Social Sciences</i>, vol. 57, no. 2, Elsevier BV, 2008, pp. 177–87, doi:<a href=\"https://doi.org/10.1016/j.mathsocsci.2008.09.004\">10.1016/j.mathsocsci.2008.09.004</a>.","ama":"Haake C-J. Two support results for the Kalai–Smorodinsky solution in small object division markets. <i>Mathematical Social Sciences</i>. 2008;57(2):177-187. doi:<a href=\"https://doi.org/10.1016/j.mathsocsci.2008.09.004\">10.1016/j.mathsocsci.2008.09.004</a>","bibtex":"@article{Haake_2008, title={Two support results for the Kalai–Smorodinsky solution in small object division markets}, volume={57}, DOI={<a href=\"https://doi.org/10.1016/j.mathsocsci.2008.09.004\">10.1016/j.mathsocsci.2008.09.004</a>}, number={2}, journal={Mathematical Social Sciences}, publisher={Elsevier BV}, author={Haake, Claus-Jochen}, year={2008}, pages={177–187} }"},"has_accepted_license":"1","status":"public","user_id":"65453","ddc":["040"],"volume":57,"page":"177-187","_id":"2506","publisher":"Elsevier BV","issue":"2","publication":"Mathematical Social Sciences","type":"journal_article","department":[{"_id":"205"},{"_id":"475"}],"file":[{"date_created":"2018-10-31T08:29:51Z","creator":"stela","content_type":"application/pdf","success":1,"file_id":"5127","date_updated":"2018-10-31T08:29:51Z","relation":"main_file","file_size":575065,"access_level":"closed","file_name":"Two support results for the Kalai–Smorodinsky solution in small object division markets.pdf"}],"date_created":"2018-04-26T10:35:57Z","publication_status":"published","date_updated":"2022-01-06T06:56:48Z","intvolume":"        57","title":"Two support results for the Kalai–Smorodinsky solution in small object division markets","year":"2008","publication_identifier":{"issn":["0165-4896"]},"author":[{"first_name":"Claus-Jochen","last_name":"Haake","full_name":"Haake, Claus-Jochen","id":"20801"}],"doi":"10.1016/j.mathsocsci.2008.09.004","language":[{"iso":"eng"}]}]