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Stable sets and standards of behaviour

Author

Listed:
  • Robert Delver

    (Department of International Security Studies, Royal Netherlands Naval Academy PO Box 10.000, 1780 CA, Den Helder, The Netherlands)

  • Herman Monsuur

    (Department of International Security Studies, Royal Netherlands Naval Academy PO Box 10.000, 1780 CA, Den Helder, The Netherlands)

Abstract

In this paper we present a constructive, behavioural and axiomatic approach to the notion of a stable set as a model of the standard of behaviour of a social organisation. The socially stable set we introduce is a generalisation of the von Neumann-Morgenstern stable set. In contrast with the original version, our stability concept is always solvable. The standard of behaviour, reflecting the established conceptual order of a society or organisation, emerges from a dominance relation on alternative conceptions that are relevant with regard to a certain issue. This common social choice phenomenon, that permeates our societies and organisations, we have tried to clarify. Two axiomatic characterisations as well as a construction algorithm for socially stable sets are presented. These characterisations are based on behavioural postulates regarding the individual or collective strategic behaviour of effective sets. Relations between socially stable sets and other notions of stability are discussed.

Suggested Citation

  • Robert Delver & Herman Monsuur, 2001. "Stable sets and standards of behaviour," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(3), pages 555-570.
    • Handle: RePEc:spr:sochwe:v:18:y:2001:i:3:p:555-570
    Note: Received: 4 May 1998/13 March 2000
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    Citations

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    Cited by:

    1. Peris, Josep E. & Subiza, Begoña, 2013. "A reformulation of von Neumann–Morgenstern stability: m-stability," Mathematical Social Sciences, Elsevier, vol. 66(1), pages 51-55.
    2. Athanasios Andrikopoulos & Nikolaos Sampanis, 2024. "A topological characterization of the existence of w-stable sets," Papers 2403.04512, arXiv.org.
    3. Monsuur, Herman, 2007. "Stable and emergent network topologies: A structural approach," European Journal of Operational Research, Elsevier, vol. 183(1), pages 432-441, November.
    4. Peris, Josep E. & Subiza, Begoña, 2012. "M-stability: A reformulation of Von Neumann-Morgenstern stability," QM&ET Working Papers 12-4, University of Alicante, D. Quantitative Methods and Economic Theory.
    5. Han, Weibin & Van Deemen, Adrian, 2016. "On the solution of w-stable sets," Mathematical Social Sciences, Elsevier, vol. 84(C), pages 87-92.
    6. Iñarra García, María Elena & Larrea Jaurrieta, María Concepción, 2005. "Admissible Hierachic Sets," IKERLANAK 2005-18, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    7. Weibin Han & Adrian Deemen & D. Ary A. Samsura, 2016. "A note on extended stable sets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(2), pages 265-275, August.
    8. Inarra, Elena & Larrea, Concepcion, 2007. "A characterization of path dependent modes of behavior," Mathematical Social Sciences, Elsevier, vol. 54(2), pages 128-136, September.
    9. Michele Gori, 2023. "Families of abstract decision problems whose admissible sets intersect in a singleton," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 61(1), pages 131-154, July.
    10. Herman Monsuur & Ton Storcken, 2004. "Centers in Connected Undirected Graphs: An Axiomatic Approach," Operations Research, INFORMS, vol. 52(1), pages 54-64, February.
    11. Iñarra García, María Elena & Larrea Jaurrieta, María Concepción, 2005. "Admissible Hierachic Sets," IKERLANAK info:eu-repo/grantAgreeme, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    12. Monsuur, Herman, 2005. "Characterizations of the 3-cycle count and backward length of a tournament," European Journal of Operational Research, Elsevier, vol. 164(3), pages 778-784, August.

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