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On the axiomatic characterization of the coalitional multinomial probabilistic values

Author

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  • Francesc Carreras

    (Universitat Politècnica de Catalunya)

  • María Albina Puente

    (Universitat Politècnica de Catalunya)

Abstract

The coalitional multinomial probabilistic values extend the notion of multinomial probabilistic value to games with a coalition structure, in such a way that they generalize the symmetric coalitional binomial semivalues and link and combine the Shapley value and the multinomial probabilistic values. By considering the property of balanced contributions within unions, a new axiomatic characterization is stated for each one of these coalitional values, provided that it is defined by a positive tendency profile, by means of a set of logically independent properties that univocally determine the value. Two applications are also shown: (a) to the Madrid Assembly in Legislature 2015–2019 and (b) to the Parliament of Andalucía in Legislature 2018–2022.

Suggested Citation

  • Francesc Carreras & María Albina Puente, 2022. "On the axiomatic characterization of the coalitional multinomial probabilistic values," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 119-151, April.
    • Handle: RePEc:spr:topjnl:v:30:y:2022:i:1:d:10.1007_s11750-021-00603-3
    DOI: 10.1007/s11750-021-00603-3
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    References listed on IDEAS

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    1. Amer, Rafael & Carreras, Francese & Gimenez, Jose Miguel, 2002. "The modified Banzhaf value for games with coalition structure: an axiomatic characterization," Mathematical Social Sciences, Elsevier, vol. 43(1), pages 45-54, January.
    2. Francesc Carreras & María Albina Puente, 2018. "A note on multinomial probabilistic values," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(1), pages 164-186, April.
    3. Dragan, Irinel, 1996. "New mathematical properties of the Banzhaf value," European Journal of Operational Research, Elsevier, vol. 95(2), pages 451-463, December.
    4. Guillermo Owen, 1975. "Multilinear extensions and the banzhaf value," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 22(4), pages 741-750, December.
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    6. Josep Freixas & M. Puente, 2002. "Reliability Importance Measures of the Components in a System Based on Semivalues and Probabilistic Values," Annals of Operations Research, Springer, vol. 109(1), pages 331-342, January.
    7. Francesc Carreras & María Albina Puente, 2006. "A Parametric Family of Mixed Coalitional Values," Lecture Notes in Economics and Mathematical Systems, in: Alberto Seeger (ed.), Recent Advances in Optimization, pages 323-339, Springer.
    8. Francesc Carreras & María Albina Puente, 2012. "Symmetric Coalitional Binomial Semivalues," Group Decision and Negotiation, Springer, vol. 21(5), pages 637-662, September.
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