An Axiomatic Approach to Proportionality between Matrices
Author
Abstract
Suggested Citation
Note: View the original document on HAL open archive server: https://hal.science/hal-00686748
Download full text from publisher
Other versions of this item:
- Gabrielle Demange & Michel L. Balinski, 1989. "An Axiomatic Approach to Proportionality between Matrices," Post-Print halshs-00670952, HAL.
References listed on IDEAS
- H. Peyton Young, 1987. "On Dividing an Amount According to Individual Claims or Liabilities," Mathematics of Operations Research, INFORMS, vol. 12(3), pages 398-414, August.
- Aumann, Robert J. & Maschler, Michael, 1985. "Game theoretic analysis of a bankruptcy problem from the Talmud," Journal of Economic Theory, Elsevier, vol. 36(2), pages 195-213, August.
Citations
Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
Cited by:
- Demange, Gabrielle, 2012.
"On party-proportional representation under district distortions,"
Mathematical Social Sciences, Elsevier, vol. 63(2), pages 181-191.
- Gabrielle Demange, 2011. "On party-proportional representation under district distortions," PSE Working Papers halshs-00623031, HAL.
- Gabrielle Demange, 2012. "On party-proportional representation under district distortions," PSE-Ecole d'économie de Paris (Postprint) halshs-00670843, HAL.
- Gabrielle Demange, 2012. "On party-proportional representation under district distortions," Post-Print halshs-00670843, HAL.
- Gabrielle Demange, 2011. "On party-proportional representation under district distortions," Working Papers halshs-00623031, HAL.
- Gabrielle Demange, 2018.
"New electoral systems and old referendums,"
PSE Working Papers
hal-01852206, HAL.
- Gabrielle Demange, 2019. "New Electoral Systems and Old Referendums," Post-Print halshs-02491873, HAL.
- Gabrielle Demange, 2018. "New electoral systems and old referendums," Working Papers hal-01852206, HAL.
- Gabrielle Demange, 2019. "New Electoral Systems and Old Referendums," PSE-Ecole d'économie de Paris (Postprint) halshs-02491873, HAL.
- Marjorie B. Gassner, 1991. "Biproportional Delegations," Journal of Theoretical Politics, , vol. 3(3), pages 321-342, July.
- Demange, Gabrielle, 2017.
"Mutual rankings,"
Mathematical Social Sciences, Elsevier, vol. 90(C), pages 35-42.
- Gabrielle Demange, 2016. "Mutual rankings," Working Papers halshs-01353825, HAL.
- Gabrielle Demange, 2017. "Mutual rankings," Post-Print halshs-01630624, HAL.
- Gabrielle Demange, 2016. "Mutual rankings," PSE Working Papers halshs-01353825, HAL.
- Gabrielle Demange, 2017. "Mutual rankings," PSE-Ecole d'économie de Paris (Postprint) halshs-01630624, HAL.
- Gabrielle Demange, 2018.
"Mechanisms in a Digitalized World,"
CESifo Working Paper Series
6984, CESifo.
- Gabrielle Demange, 2019. "Mechanisms in a digitalized world," Post-Print hal-01715951, HAL.
- Gabrielle Demange, 2019. "Mechanisms in a digitalized world," PSE-Ecole d'économie de Paris (Postprint) hal-01715951, HAL.
- Gabrielle Demange, 2013.
"On Allocating Seats To Parties And Districts: Apportionments,"
International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 15(03), pages 1-14.
- Gabrielle Demange, 2011. "On allocating seats to parties and districts: apportionments," PSE Working Papers halshs-00644439, HAL.
- Gabrielle Demange, 2011. "On allocating seats to parties and districts: apportionments," Working Papers halshs-00644439, HAL.
- Gabrielle Demange, 2013. "On allocating seats to parties and districts: apportionments," Post-Print halshs-00879779, HAL.
- Gabrielle Demange, 2013. "On allocating seats to parties and districts: apportionments," PSE-Ecole d'économie de Paris (Postprint) halshs-00879779, HAL.
- Attila Tasnádi, 2008. "The extent of the population paradox in the Hungarian electoral system," Public Choice, Springer, vol. 134(3), pages 293-305, March.
- Oelbermann, Kai-Friederike, 2016. "Alternate Scaling algorithm for biproportional divisor methods," Mathematical Social Sciences, Elsevier, vol. 80(C), pages 25-32.
- Isabella Lari & Federica Ricca & Andrea Scozzari, 2014. "Bidimensional allocation of seats via zero-one matrices with given line sums," Annals of Operations Research, Springer, vol. 215(1), pages 165-181, April.
- ,, 2014.
"A ranking method based on handicaps,"
Theoretical Economics, Econometric Society, vol. 9(3), September.
- Gabrielle Demange, 2013. "A ranking method based on handicaps," Working Papers halshs-00687180, HAL.
- Gabrielle Demange, 2014. "A ranking method based on handicaps," PSE-Ecole d'économie de Paris (Postprint) halshs-01109087, HAL.
- Gabrielle Demange, 2014. "A Ranking Method Based on Handicaps," CESifo Working Paper Series 4636, CESifo.
- Gabrielle Demange, 2013. "A ranking method based on handicaps," PSE Working Papers halshs-00687180, HAL.
- Gabrielle Demange, 2014. "A ranking method based on handicaps," Post-Print halshs-01109087, HAL.
- Gabrielle Demange, 2021.
"On the resolution of cross-liabilities,"
Working Papers
halshs-03151128, HAL.
- Gabrielle Demange, 2024. "On the resolution of cross-liabilities," PSE-Ecole d'économie de Paris (Postprint) halshs-04156110, HAL.
- Gabrielle Demange, 2024. "On the resolution of cross-liabilities," Post-Print halshs-04156110, HAL.
- Gabrielle Demange, 2021. "On the resolution of cross-liabilities," PSE Working Papers halshs-03151128, HAL.
- Michel L. Balinski & Gabrielle Demange, 1989. "Algorithm for Proportional Matrices in Reals and Integers," Post-Print halshs-00585327, HAL.
- Ricca, Federica & Scozzari, Andrea & Simeone, Bruno, 2011. "The give-up problem for blocked regional lists with multi-winners," Mathematical Social Sciences, Elsevier, vol. 62(1), pages 14-24, July.
- Moulin, Herve, 2017. "Consistent bilateral assignment," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 43-55.
- Federica Ricca & Andrea Scozzari & Paolo Serafini & Bruno Simeone, 2012. "Error minimization methods in biproportional apportionment," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(3), pages 547-577, October.
- Michel Balinski, 2007. "Equitable representation and recruitment," Annals of Operations Research, Springer, vol. 149(1), pages 27-36, February.
- Gabrielle Demange, 2020. "Resolution rules in a system of financially linked firms," Working Papers hal-02502413, HAL.
- Victoriano Ramírez-González & Blanca Delgado-Márquez & Antonio Palomares & Adolfo López-Carmona, 2014. "Evaluation and possible improvements of the Swedish electoral system," Annals of Operations Research, Springer, vol. 215(1), pages 285-307, April.
- Paolo Serafini & Bruno Simeone, 2012. "Certificates of optimality: the third way to biproportional apportionment," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(2), pages 247-268, February.
- MESNARD, Louis de, 1999. "Interpretation of the RAS method : absorption and fabrication effects are incorrect," LATEC - Document de travail - Economie (1991-2003) 9907, LATEC, Laboratoire d'Analyse et des Techniques EConomiques, CNRS UMR 5118, Université de Bourgogne.
- Paolo Serafini, 2015. "Certificates of optimality for minimum norm biproportional apportionments," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(1), pages 1-12, January.
- Moulin, Hervé, 2016. "Entropy, desegregation, and proportional rationing," Journal of Economic Theory, Elsevier, vol. 162(C), pages 1-20.
- Friedrich Pukelsheim, 2014. "Biproportional scaling of matrices and the iterative proportional fitting procedure," Annals of Operations Research, Springer, vol. 215(1), pages 269-283, April.
- Gaffke, Norbert & Pukelsheim, Friedrich, 2008. "Divisor methods for proportional representation systems: An optimization approach to vector and matrix apportionment problems," Mathematical Social Sciences, Elsevier, vol. 56(2), pages 166-184, September.
Most related items
These are the items that most often cite the same works as this one and are cited by the same works as this one.- William Thomson, 2007.
"On the existence of consistent rules to adjudicate conflicting claims: a constructive geometric approach,"
Review of Economic Design, Springer;Society for Economic Design, vol. 11(3), pages 225-251, November.
- William Thomson, 2006. "On the Existence of Consistent Rules to Adjudicate Conflicting Claims: A Constructive Geometric Approach," RCER Working Papers 528, University of Rochester - Center for Economic Research (RCER).
- Juan Moreno-Ternero & Antonio Villar, 2006.
"The TAL-Family of Rules for Bankruptcy Problems,"
Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 27(2), pages 231-249, October.
- Antonio Villar Notario & Juan D. Moreno Ternero, 2001. "The Tal-Family Of Rules For Bankruptcy Problems," Working Papers. Serie AD 2001-33, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
- MORENO-TERNERO, Juan D. & VILLAR, Antonio, 2006. "The TAL-family or rules for bankruptcy problems," LIDAM Reprints CORE 1897, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Erik Ansink & Hans-Peter Weikard, 2012.
"Sequential sharing rules for river sharing problems,"
Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(2), pages 187-210, February.
- Erik Ansink & Hans-Peter Weikard, 2009. "Sequential Sharing Rules for River Sharing Problems," Working Papers 2009.114, Fondazione Eni Enrico Mattei.
- Jingyi Xue, 2018. "Fair division with uncertain needs," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(1), pages 105-136, June.
- Lahiri, Somdeb, 2001.
"Axiomatic characterizations of the CEA solution for rationing problems,"
European Journal of Operational Research, Elsevier, vol. 131(1), pages 162-170, May.
- Lahiri Somdeb, 1999. "Axiomatic Characterizations of the CEA Solution for Rationing Problems," IIMA Working Papers WP1999-02-03, Indian Institute of Management Ahmedabad, Research and Publication Department.
- Bas Dietzenbacher & Yuki Tamura & William Thomson, 2024.
"Partial-implementation invariance and claims problems,"
Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 63(1), pages 203-229, August.
- Dietzenbacher, Bas & Tamura, Yuki & Thomson, William, 2023. "Partial-implementation invariance and claims problems," Research Memorandum 002, Maastricht University, Graduate School of Business and Economics (GSBE).
- Sanchez-Soriano, Joaquin, 2021. "Families of sequential priority rules and random arrival rules with withdrawal limits," Mathematical Social Sciences, Elsevier, vol. 113(C), pages 136-148.
- Peris, Josep E. & Jiménez-Gómez, José M., 2012.
"A Proportional Approach to Bankruptcy Problems with a guaranteed minimum,"
QM&ET Working Papers
12-7, University of Alicante, D. Quantitative Methods and Economic Theory.
- Giménez-Gómez, José Manuel & Peris, Josep E., 2012. "A Proportional Approach to Bankruptcy Problems with a guaranteed minimum," Working Papers 2072/182645, Universitat Rovira i Virgili, Department of Economics.
- José M. Jiménez Gómez & Josep Enric Peris Ferrando, 2012. "A proportional approach to bankruptcy. Problems with a guaranteed minimum," Working Papers. Serie AD 2012-11, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
- Hougaard, Jens Leth & Moreno-Ternero, Juan D. & Østerdal, Lars Peter, 2012.
"A unifying framework for the problem of adjudicating conflicting claims,"
Journal of Mathematical Economics, Elsevier, vol. 48(2), pages 107-114.
- Jens L. Hougaard & Juan D. Moreno-Ternero & Lars P. Østerdal, 2011. "A unifying framework for the problem of adjudicating conflicting claims," Working Papers 2011-03, Universidad de Málaga, Department of Economic Theory, Málaga Economic Theory Research Center.
- Jens L. Hougaard & Juan D. Moreno-Ternero & Lars P. Østerdal, 2011. "A Unifying Framework for the Problem of Adjudicating Conflicting Claims," Discussion Papers 11-03, University of Copenhagen. Department of Economics.
- Jens L. Hougaard & Juan D. Moreno-Ternero & Lars P. Osterdal, 2012. "A unifying framework for the problem of adjudicating conflicting claims," Working Papers 12.01, Universidad Pablo de Olavide, Department of Economics.
- Jens Leth Hougaard & Juan D. Moreno-Ternero & Lars Peter Østerdal, 2011. "A unifying framework for the problem of adjudicating conflicting claims," MSAP Working Paper Series 01_2011, University of Copenhagen, Department of Food and Resource Economics.
- HOUGAARD, Jens Leth & MORENO-TERNERO, Juan D. & OSTERDAL, Lars Peter, 2012. "A unifying framework for the problem of adjudicating conflicting claims," LIDAM Reprints CORE 2399, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- HOUGAARD, Jens L. & MORENO-TERNERO, Juan D. & OSTERDAL, Lars P., 2011. "A unifying framework for the problem of adjudicating conflicting claims," LIDAM Discussion Papers CORE 2011071, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- William Thomson, 2011.
"Consistency and its converse: an introduction,"
Review of Economic Design, Springer;Society for Economic Design, vol. 15(4), pages 257-291, December.
- Thomson, W., 1998. "Consistency and its Converse: an Introduction," RCER Working Papers 448, University of Rochester - Center for Economic Research (RCER).
- William Thomson, 2014. "Compromising between the proportional and constrained equal awards rules," RCER Working Papers 584, University of Rochester - Center for Economic Research (RCER).
- repec:ebl:ecbull:v:3:y:2008:i:56:p:1-10 is not listed on IDEAS
- Miguel Ángel Mirás Calvo & Carmen Quinteiro Sandomingo & Estela Sánchez-Rodríguez, 2022. "The average-of-awards rule for claims problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 59(4), pages 863-888, November.
- Herrero, Carmen & Maschler, Michael & Villar, Antonio, 1999.
"Individual rights and collective responsibility: the rights-egalitarian solution,"
Mathematical Social Sciences, Elsevier, vol. 37(1), pages 59-77, January.
- Antonio Villar Notario & Carmen Herrero Blanco & Michael Maschler, 1996. "Individual rights and collective responsibility: The rights-egalitarian solution," Working Papers. Serie AD 1996-04, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
- Chambers, Christopher P., 2006. "Asymmetric rules for claims problems without homogeneity," Games and Economic Behavior, Elsevier, vol. 54(2), pages 241-260, February.
- Jaume García-Segarra & Miguel Ginés-Vilar, 2023. "Additive adjudication of conflicting claims," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(1), pages 93-116, March.
- Rodica Branzei & Sirma Zeynep Alparslan Gok, 2008. "Bankruptcy problems with interval uncertainty," Economics Bulletin, AccessEcon, vol. 3(56), pages 1-10.
- Hervé Moulin & Jay Sethuraman, 2013. "The Bipartite Rationing Problem," Operations Research, INFORMS, vol. 61(5), pages 1087-1100, October.
- Gallo, Oihane & Inarra, Elena, 2018. "Rationing rules and stable coalition structures," Theoretical Economics, Econometric Society, vol. 13(3), September.
- Patrick Harless, 2017. "Endowment additivity and the weighted proportional rules for adjudicating conflicting claims," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(3), pages 755-781, March.
- Moreno-Ternero, Juan D. & Villar, Antonio, 2004.
"The Talmud rule and the securement of agents' awards,"
Mathematical Social Sciences, Elsevier, vol. 47(2), pages 245-257, March.
- Juan de Dios Moreno Ternero & Antonio Villar Notario, 2003. "The Talmud Rule And The Securement Of Agents? Awards," Working Papers. Serie AD 2003-05, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
More about this item
Keywords
axiomatics; fairness; optimality; scaling; allocation; apportionment; contingency; rounding;All these keywords.
Statistics
Access and download statisticsCorrections
All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:journl:hal-00686748. See general information about how to correct material in RePEc.
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .
Please note that corrections may take a couple of weeks to filter through the various RePEc services.