IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v320y2023i1d10.1007_s10479-022-05044-0.html
   My bibliography  Save this article

On stratified sampling for estimating coalitional values

Author

Listed:
  • A. Saavedra-Nieves

    (Universidade de Santiago de Compostela)

Abstract

This paper addresses two sampling methodologies to respectively estimate the Owen value and the Banzhaf–Owen value for TU-games with a priori unions. Both proposals are based on stratified sampling on the set of those coalitions that are compatible with the system of unions according to their cardinalities. These sampling methodologies are analysed in terms of the theoretical properties and of the establishment of bounds for the absolute error from a statistical point of view. Finally, we evaluate the performance of these tools on several real well-known examples in the literature.

Suggested Citation

  • A. Saavedra-Nieves, 2023. "On stratified sampling for estimating coalitional values," Annals of Operations Research, Springer, vol. 320(1), pages 325-353, January.
    • Handle: RePEc:spr:annopr:v:320:y:2023:i:1:d:10.1007_s10479-022-05044-0
    DOI: 10.1007/s10479-022-05044-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-022-05044-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10479-022-05044-0?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Dennis Leech, 2002. "Voting Power in the Governance of the International Monetary Fund," Annals of Operations Research, Springer, vol. 109(1), pages 375-397, January.
    2. Peter Borm & Luisa Carpente & Balbina Casas-Méndez & Ruud Hendrickx, 2005. "The Constrained Equal Awards Rule for Bankruptcy Problems with a Priori Unions," Annals of Operations Research, Springer, vol. 137(1), pages 211-227, July.
    3. Stefano Moretti & Fioravante Patrone & Stefano Bonassi, 2007. "The class of microarray games and the relevance index for genes," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(2), pages 256-280, December.
    4. Algaba, E. & Bilbao, J.M. & Fernandez, J.R., 2007. "The distribution of power in the European Constitution," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1752-1766, February.
    5. Benati, Stefano & López-Blázquez, Fernando & Puerto, Justo, 2019. "A stochastic approach to approximate values in cooperative games," European Journal of Operational Research, Elsevier, vol. 279(1), pages 93-106.
    6. Leech, Dennis, 2002. "Voting Power In The Governance Of The International Monetary Fund," Economic Research Papers 269354, University of Warwick - Department of Economics.
    7. Guillermo Owen, 1975. "Multilinear extensions and the banzhaf value," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 22(4), pages 741-750, December.
    8. S. C. Littlechild & G. Owen, 1973. "A Simple Expression for the Shapley Value in a Special Case," Management Science, INFORMS, vol. 20(3), pages 370-372, November.
    9. Alonso-Meijide, J.M. & Bilbao, J.M. & Casas-Méndez, B. & Fernández, J.R., 2009. "Weighted multiple majority games with unions: Generating functions and applications to the European Union," European Journal of Operational Research, Elsevier, vol. 198(2), pages 530-544, October.
    10. Xiaotie Deng & Christos H. Papadimitriou, 1994. "On the Complexity of Cooperative Solution Concepts," Mathematics of Operations Research, INFORMS, vol. 19(2), pages 257-266, May.
    11. A. Saavedra-Nieves & M. G. Fiestras-Janeiro, 2021. "Sampling methods to estimate the Banzhaf–Owen value," Annals of Operations Research, Springer, vol. 301(1), pages 199-223, June.
    12. Saavedra-Nieves, Alejandro & Saavedra-Nieves, Paula, 2020. "On systems of quotas from bankruptcy perspective: the sampling estimation of the random arrival rule," European Journal of Operational Research, Elsevier, vol. 285(2), pages 655-669.
    13. J. Alonso-Meijide & C. Bowles, 2005. "Generating Functions for Coalitional Power Indices: An Application to the IMF," Annals of Operations Research, Springer, vol. 137(1), pages 21-44, July.
    14. Dennis Leech, 2003. "Computing Power Indices for Large Voting Games," Management Science, INFORMS, vol. 49(6), pages 831-837, June.
    15. Algaba, E. & Bilbao, J. M. & Fernandez Garcia, J. R. & Lopez, J. J., 2003. "Computing power indices in weighted multiple majority games," Mathematical Social Sciences, Elsevier, vol. 46(1), pages 63-80, August.
    16. Guillermo Owen, 1972. "Multilinear Extensions of Games," Management Science, INFORMS, vol. 18(5-Part-2), pages 64-79, January.
    17. Silvia Lorenzo-Freire, 2017. "New characterizations of the Owen and Banzhaf–Owen values using the intracoalitional balanced contributions property," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(3), pages 579-600, October.
    Full references (including those not matched with items on IDEAS)

    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.
    1. A. Saavedra-Nieves & M. G. Fiestras-Janeiro, 2021. "Sampling methods to estimate the Banzhaf–Owen value," Annals of Operations Research, Springer, vol. 301(1), pages 199-223, June.
    2. Michela Chessa, 2014. "A generating functions approach for computing the Public Good index efficiently," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 658-673, July.
    3. Hamers, Herbert & Husslage, Bart & Lindelauf, R. & Campen, Tjeerd, 2016. "A New Approximation Method for the Shapley Value Applied to the WTC 9/11 Terrorist Attack," Other publications TiSEM 8a67b416-1091-4efe-a1a6-7, Tilburg University, School of Economics and Management.
    4. Hamers, Herbert & Husslage, Bart & Lindelauf, R. & Campen, Tjeerd, 2016. "A New Approximation Method for the Shapley Value Applied to the WTC 9/11 Terrorist Attack," Discussion Paper 2016-042, Tilburg University, Center for Economic Research.
    5. Yuto Ushioda & Masato Tanaka & Tomomi Matsui, 2022. "Monte Carlo Methods for the Shapley–Shubik Power Index," Games, MDPI, vol. 13(3), pages 1-14, June.
    6. Alonso-Meijide, J.M. & Bilbao, J.M. & Casas-Méndez, B. & Fernández, J.R., 2009. "Weighted multiple majority games with unions: Generating functions and applications to the European Union," European Journal of Operational Research, Elsevier, vol. 198(2), pages 530-544, October.
    7. Antônio Francisco Neto & Carolina Rodrigues Fonseca, 2019. "An approach via generating functions to compute power indices of multiple weighted voting games with incompatible players," Annals of Operations Research, Springer, vol. 279(1), pages 221-249, August.
    8. Hang Luo & Lize Yang & Kourosh Houshmand, 2021. "Power Structure Dynamics in Growing Multilateral Development Banks: The Case of the Asian Infrastructure Investment Bank," Global Policy, London School of Economics and Political Science, vol. 12(1), pages 24-39, February.
    9. Alexander Mayer & Stefan Napel, 2020. "Weighted voting on the IMF Managing Director," Economics of Governance, Springer, vol. 21(3), pages 237-244, September.
    10. Sylvain Béal & Marc Deschamps & Mostapha Diss & Issofa Moyouwou, 2022. "Inconsistent weighting in weighted voting games," Public Choice, Springer, vol. 191(1), pages 75-103, April.
    11. Wilms, Ingo, 2020. "Dynamic programming algorithms for computing power indices in weighted multi-tier games," Mathematical Social Sciences, Elsevier, vol. 108(C), pages 175-192.
    12. Hang Luo & Lize Yang, 2021. "Equality and Equity in Emerging Multilateral Financial Institutions: The Case of the BRICS Institutions," Global Policy, London School of Economics and Political Science, vol. 12(4), pages 482-508, September.
    13. André Casajus & Frank Huettner, 2019. "The Coleman–Shapley index: being decisive within the coalition of the interested," Public Choice, Springer, vol. 181(3), pages 275-289, December.
    14. Leech, Dennis, 2010. "Power Indices in Large Voting Bodies," Economic Research Papers 270996, University of Warwick - Department of Economics.
    15. Josep Freixas & Roberto Lucchetti, 2016. "Power in voting rules with abstention: an axiomatization of a two components power index," Annals of Operations Research, Springer, vol. 244(2), pages 455-474, September.
    16. Julien Reynaud & Fabien Lange & Łukasz Gątarek & Christian Thimann, 2011. "Proximity in Coalition Building," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 3(3), pages 111-132, September.
    17. Benati, Stefano & Rizzi, Romeo & Tovey, Craig, 2015. "The complexity of power indexes with graph restricted coalitions," Mathematical Social Sciences, Elsevier, vol. 76(C), pages 53-63.
    18. Stefano Benati & Giuseppe Vittucci Marzetti, 2021. "Voting power on a graph connected political space with an application to decision-making in the Council of the European Union," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(4), pages 733-761, November.
    19. Taylan Mavruk & Conny Overland & Stefan Sjögren, 2020. "Keeping it real or keeping it simple? Ownership concentration measures compared," European Financial Management, European Financial Management Association, vol. 26(4), pages 958-1005, September.
    20. Pavel Doležel, 2011. "Optimizing the Efficiency of Weighted Voting Games," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 5(3), pages 306-323, November.

    Corrections

    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:spr:annopr:v:320:y:2023:i:1:d:10.1007_s10479-022-05044-0. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.