A Proportional Rule for the Division Problems with Multiple References: An Application to the Problems of Probability Aggregation and Probability Updating
DOI:
https://doi.org/10.46661/revmetodoscuanteconempresa.2105Keywords:
Problemas de división con referencias múltiples, regla proporcional ponderada, agregación y actualización de probabilidades, division problems with multiple references, weighted proportional rule, probability aggregation, probability updating.Abstract
In this paper we extend the proportional rule to division problems with multiple references and we present a result of characterization of the weighted proportional rule. As a particular case, we analyze the problems of probability aggregation and probability updating.
Downloads
References
Bergantiños, G.; Lorenzo, L.; Lorenzo-Freire, S. (2010) "A characterization of the proportional rule in multi-issue allocation situations". Operations Research Letters 38, 17-19.
Bergantiños, G.; Lorenzo, L.; Lorenzo-Freire, S. (2008) "New characterizations of the constrained equal awards rule in multi-issue allocation situations". Mimeo, University of Vigo.
Branzei, R.; Dimitrov, D.; Pickl, S; Tijs, S. (2004) "How to cope with division problems under interval uncertainty claims?". International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 12, 191-200.
Calleja, P.; Borm, P.; Hendrickx, R. (2005) "Multi-issue allocation situations". European Journal of Operational Research 164, 730-747.
Chun, Y. (1988a) "The proportional solution for rights problem". Mathematical Social Sciences 15, 231-246.
Gilboa, I.; Schmeidler, D. (1993) "Updating ambiguous beliefs". J. Econ. Theory 59, 33-49.
González-Alcón, C.; Borm, P.; Hendrickx, R. (2007) "A composite run to the bank rule for multi-issue allocation situations". Mathematical Methods of Operations Research 65, 339-352.
Ju, B.G.; Miyagawa, E. (2002) "Proportionality and non-manipulability in claims problems". Mimeo.
Ju, B.G., Miyagawa, E.; Sakai, T. (2007) "Non-manipulable division rules in claim problems and generalizations". Journal of Economic Theory 132, 1-26.
Lorenzo-Freire, S.; Casas-Méndez, B.; Hendrickx, R. (2009) "The two-stage constrained equal awards and losses rules for multi-issue allocation situations". Top.
Majumdar, D. (2004) "An axiomatic charaterization of Bayes' rule". Math. Soc. Sci. 47, 261-273.
McConway, K.J. (1981) "Marginalization and Liear Opinion Pools". J. Amer. Statis. Assoc. 76, 410-414.
Moreno-Ternero, J. (2009) "The proportional rule for multi-issue banckrupty problems". Economics Bulletin 29, 483-490.
Moulin, H. (1985b) "The separability axiom and equal-sharing methods". Journal of Economics Theory 36, 120-148.
Pulido, M.; Sánchez-Soriano, J.; Llorca, N. (2002) "Game theory techniques for university management: an extended bankruptcy model". Annals of Operations Research 109, 129-142.
Pulido, M.; Borm, P.; Hendrickx, R.; Llorca, N.; Sánchez-Soriano, J. (2008) "Compromise solutions for bankruptcy situations with references". Annals of Operations Research 158, 133-141.
Rubinstein, A.; Fishburn, P.C. (1986) "Algebraic aggregation theory". J. Econ. Theory 38, 63-77.
Thomson, W. (2003) "How to divide when there isn't enough: from the Talmud to modern game theory". University of Rochester.
Young, P. (1988) "Distributive justice in taxation". Journal of Economic Theory 44, 321-335.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2011 Revista de Métodos Cuantitativos para la Economía y la Empresa
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Submission of manuscripts implies that the work described has not been published before (except in the form of an abstract or as part of thesis), that it is not under consideration for publication elsewhere and that, in case of acceptance, the authors agree to automatic transfer of the copyright to the Journal for its publication and dissemination. Authors retain the authors' right to use and share the article according to a personal or instutional use or scholarly sharing purposes; in addition, they retain patent, trademark and other intellectual property rights (including research data).
All the articles are published in the Journal under the Creative Commons license CC-BY-SA (Attribution-ShareAlike). It is allowed a commercial use of the work (always including the author attribution) and other derivative works, which must be released under the same license as the original work.
Up to Volume 21, this Journal has been licensing the articles under the Creative Commons license CC-BY-SA 3.0 ES. Starting from Volume 22, the Creative Commons license CC-BY-SA 4.0 is used.