---
_id: '56420'
abstract:
- lang: eng
  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.
article_type: original
author:
- first_name: Nadja
  full_name: Stroh-Maraun, Nadja
  id: '13264'
  last_name: Stroh-Maraun
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>
  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>
  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} }'
  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>.'
  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>.'
  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>.
  short: N. Stroh-Maraun, Mathematical Social Sciences 132 (2024) 49–56.
date_created: 2024-10-08T11:52:59Z
date_updated: 2025-02-28T11:33:48Z
ddc:
- '330'
department:
- _id: '200'
doi: 10.1016/j.mathsocsci.2024.09.001
file:
- access_level: closed
  content_type: application/pdf
  creator: nmaraun
  date_created: 2024-10-08T11:53:39Z
  date_updated: 2024-10-08T11:53:39Z
  file_id: '56421'
  file_name: 1-s2.0-S0165489624000817-main.pdf
  file_size: 611017
  relation: main_file
  success: 1
file_date_updated: 2024-10-08T11:53:39Z
funded_apc: '1'
has_accepted_license: '1'
intvolume: '       132'
jel:
- C78
- D47
keyword:
- Matching
- School choice
- College admission problems
- Top trading cycles
- Pareto efficiency
- Strategy-proofness
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://www.sciencedirect.com/science/article/pii/S0165489624000817?via%3Dihub
oa: '1'
page: 49-56
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'
publication: Mathematical Social Sciences
publication_identifier:
  issn:
  - 0165-4896
publication_status: published
publisher: Elsevier BV
status: public
title: Weighted school choice problems and the weighted top trading cycles mechanism
type: journal_article
user_id: '477'
volume: 132
year: '2024'
...
---
_id: '2506'
author:
- first_name: Claus-Jochen
  full_name: Haake, Claus-Jochen
  id: '20801'
  last_name: Haake
citation:
  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>
  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>
  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} }'
  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>.'
  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.
  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>.
  short: C.-J. Haake, Mathematical Social Sciences 57 (2008) 177–187.
date_created: 2018-04-26T10:35:57Z
date_updated: 2022-01-06T06:56:48Z
ddc:
- '040'
department:
- _id: '205'
- _id: '475'
doi: 10.1016/j.mathsocsci.2008.09.004
file:
- access_level: closed
  content_type: application/pdf
  creator: stela
  date_created: 2018-10-31T08:29:51Z
  date_updated: 2018-10-31T08:29:51Z
  file_id: '5127'
  file_name: Two support results for the Kalai–Smorodinsky solution in small object
    division markets.pdf
  file_size: 575065
  relation: main_file
  success: 1
file_date_updated: 2018-10-31T08:29:51Z
has_accepted_license: '1'
intvolume: '        57'
issue: '2'
language:
- iso: eng
page: 177-187
publication: Mathematical Social Sciences
publication_identifier:
  issn:
  - 0165-4896
publication_status: published
publisher: Elsevier BV
status: public
title: Two support results for the Kalai–Smorodinsky solution in small object division
  markets
type: journal_article
user_id: '65453'
volume: 57
year: '2008'
...