Fair Division: Corrected Proportional Rule
DOI:
https://doi.org/10.26821/IJSHRE.13.08.2025.130602Keywords:
Corrected proportional rule, Fair division, Divisible resources, Clustering, Réduction if inequalities, Process, Taguchi MethodAbstract
In this paper, we intend to present and apply the Corrected Proportional rule (PCo) as a fair division rule in its own right, which constitutes with the methods PRRC (Resources Distribution Process based on the results of the Clustering) and PRRG (Resources Distribution Process at Group level) the three main methods of the Fair Division Approach based on Clustering and Reduction of inequalities (APCR). The PCo rule reduces inequalities between individuals to a single level, that of classes considered, each, as a population in its own right. The originality of this paper is due to the fact that PCo rule is a fair division rule in its own right because of its results and is not used at all in the literature.
References
K. Acosta-Vega Rick, A. Encarnacion, J. Sanchez-Soriano, On priority in multi-issue bankruptcy problems with crossed claims, arXiv :2205.00450v2 [math.OC], September 23, 2022.
R. J. Aumann, M. Mascheler, « Game theoretic analysis of a bankruptcy problem from the Talmud. »J Econ Theory 36, 1985, pp 195-213
E. Autant, « Le partage: nouveau paradigme? » Dans revue de MAUSS, 2010/1 n°35.
Béatrice de Tilière, Analyse Statistiques Multivariée, 2009 (http://proba.jussien.fr/detiline/cours/polycop-Bio.pdf, consulté le 20/02/2016).
Boyer Marcel et al. , Partage des coûts et tarification des infrastructures, CIRANO, Quebec, 2006
M. Chavent et al. , Classification des modalités d’une variable qualitative : approche symbolique et application en écotoxicologie, 7è rencontre de la textit{société Francophone de Classsification (SFC)}, Nance, 1999, 35-41.
M. Forse et M. Parodi, « Perception des inégalités économiques et sentiment de justice sociale », Revue de l’OFCE, 2007/3 (n°102), 2007, pages 483-540 ,
F. Husson et J. Josse. Analyse de données avec R, Complémentarité des méthodes d’Analyse Factorielle et de Classification, Agrocampus Rennes, Marseille, 2010.
C. Klamler, fair division, university of Graz, Austria, 2010 (www.researchgate.net consulté le 25 sept 2022)
M. Lemaître M, Partages et allocations équitables, cours, 2016 (https ://sites.google.com /site/michellemaitre31/enseignement).
J. Mazerolle Marc, Programmation avec R – notions générales, Statistiques appliquées aux sciences, SCI 1018, Institut de recherche sur les forêts, Université du Québec en Abitibi-Témiscamingue, © TÉLUQ, 2013 Québec.
Miguel Angel Miras Calvo and al., Lago Nunez Lugilde, Carmen Quinteiro Sandomingo, Estela Sanchez-Rodriguez , The adjusted proportional and the minimal overlap rules restricted to the lower-half, higher-half, and middde domains, ECOBAS, 2021-02., 2021.
J. D. Moreno-Ternero.The proportional rule for multi-issue bankruptcy problems, Core Discussion paper, 2006/76, 2006.
D.-R. Mputu Losala Lomo, Application de la Classification Ascendante Hiérarchique à la Répartition des Ressources Budgétaires dans la ville province de Kinshasa, Dissertation DEA, UPN, Kinshasa, 2022. (https ://mpra.ub.uni muenchen.de/113774/, Consulté le 09/12/2022))
D.-R. Mputu Losala Lomo, The clustering method applied in a fair division process, International Journal of Scientific Research and Innovative Technology (IJSRIT), vol. 10, Issue 1, March, 1-29, 2023.
D.-R. Mputu Losala Lomo , Fair division approach based on clustering and reduction of inequalities, iJournals :International Journal of Software and Hardware Research in Engineering (IJSHRE), Volume 12, Issue 3, March, pp 14-28 , 2024. (https://ijournals.in/journal/index.php/ijshre/article/view/237, Consulté le 15/04/2024 à 20h00')
M. Pulido, J. Sanchez-Soriano, and N. Llorca, Game theoric techniques for university management : an extended bankruptcy model, Annals of Operations Research, 109, 129-142, 2002.
M. Pulido et al., Compromise solutions for bankruptcy situations with references, Annals of Operations Research 158, 133-141, 2008.
Quant Marieke, Borm Peter et Maaten Rogier, A concede-and-divide rule for bankruptcy problems, CenTER Discussion Paper, vol.2005-20,2005.
M. Sheikhmohammady and K. Madani , Sharing a multi-national resource through bankruptcy procedures, World environmental and Water Resources Congress, Ahupua’a, 2008.
L. Sousa and J. Gama, The application of hierarchical clustering algorithms for recognition using Biometrics of the hand, IJAERS, vol-1, Issue 7, december, 2014.
J.-H. Sublemontier, Classification non supervisée : de la multiplicité des données à la multiplicité des analyses, Thèse, Université d’Orléans, 2012.
W. Thomson, Game-theoretic analysis of bankruptcy and taxation problems : a survey Math. Soc. Sci 45, 249-297, 2003.
W. Thomson , Axiomatic and game-theoretic analysis of bankruptcy and taxation problems : an update, Rochester Center for Economic Research, University of Rochester, Working Paper No. 578, August, 2013.
Tran Dinh Khang et al., Fuzzy C-Means Clustering algorithm with multiple fuzzification coefficients, MDPI, Algorithms, 13, 158, 2020. (www.mdpi.com/journal/algorithms) (https://www.mdpi.com/1999-4893/13/7/158/htm, consulté le 22/05/2022)
X. L. Xie and G. A. Beni, Validity measure for fuzzy clustering, IEEE transactions on pattern analysis and machine intelligence, vol. 13, n°8, august, 841-846, 1991.
