The Strategy of Third-Party Mediation Based on the Option Prioritization in the Graph Model

Abstract

The resolution of real-world conflicts is often supported by third-party intervention (i.e., mediation). This paper proposes a possible mediation support in the form of a reverse optimization procedure under the framework of the Graph Model for Conflict Resolution (GMCR). The approach computes minimal priority adjustments of preference statements that are necessary to achieve a desired agreement. A mathematical model, based on the matrix form of GMCR, is developed to analyze this third-party mediation problem. Thereby, this study makes a first attempt to obtain option-based mediation strategies, which add comprehensiveness to the traditional state-based strategies, yet are easier to understand and hence more acceptable to the conflict participants. To illustrate the practicality, the proposed procedure is applied to a medical dispute between a patient and a hospital, with the aim to suggest changes in the ordering of preference statements that lead to a desired outcome.

Keywords

Graph Model for Conflict Resolution / third party / mediation / option prioritization / minimal adjustment

References

[1] Balas E, Jeroslow R. Canonical cuts on the unit hypercube. SIAM Journal on Applied Mathematics, 1972, 23(1): 61-69.

[2] Bove V, Gleditsch KS, Sekeris PG. “Oil above water”: Economic interdependence and third-party intervention. Journal of Conflict Resolution, 2016, 60(7): 1251-1277.

[3] Chang YM, Luo Z, Zhang Y. The timing of third-party intervention in social conflict. Defence and Peace Economics, 2018, 29(2): 91-110.

[4] Channel PO. 42 cases of typical meidical disputes since 2016, 2016

[5] Fang L, Hipel KW, Kilgour DM. Conflict models in graph form: Solution concepts and their interrelationships. European Journal of Operational Research, 1989, 41(1): 86-100.

[6] Fang L, Hipel KW, Kilgour DM. Interactive Decision Making: The Graph Model for Conflict Resolution, 1993, New York, USA: Wiley

[7] Fang L, Hipel KW, Kilgour DM, Peng X. A decision support system for interactive decision making - part I: Model formulation. Systems Man & Cybernetics Part C Applications & Reviews IEEE Transactions on, 2003, 33(1): 42-55.

[8] Fang L, Hipel KW, Kilgour DM, Peng X. A decision support system for interactive decision making-part II: Analysis and output interpretation. Systems Man & Cybernetics Part C Applications & Reviews IEEE Transactions on, 2003, 33(1): 56-66.

[9] Fenn P, Lowe D, Speck C. Conflict and dispute in construction. Construction Management and Economics, 1997, 15(6): 513-518.

[10] Findley MG, Marineau JF. Lootable resources and third-party intervention into civil wars. Conflict Management and Peace Science, 2015, 32(5): 465-486.

[11] Fisher R. Methods of Third-party Intervention, 2001, Berlin, Germany: Berghof Research Center for Constructive Conflict Management

[12] Fraser NM, Hipel KW. Solving complex conflicts. IEEE Transactions on Systems Man & Cybernetics, 1979, 9(12): 805-816.

[13] Fraser NM, Hipel KW. Conflict Analysis: Models and Resolutions, 1984, Amsterdam, Netherlands: North-Holland.

[14] Garcia A, Obeidi A, Hipel KW. Strategic advice for decision-making under conflict based on observed behaviour, 2018, 332: 96-104.

[15] Greig JM, Diehl PF. Softening up: Making conflicts more amenable to diplomacy. International Interactions, 2006, 32(4): 355-384.

[16] Han Q, Zhu Y, Ke GY, Lin H. A two-stage decision framework for resolving brownfield conflicts. International Journal of Environmental Research and Public Health, 2019, 16(6): 1039.

[17] Hou Y, Jiang Y, Xu H. Option prioritization for three-level preference in the graph model for conflict resolution. International Conference on Group Decision and Negotiation, Warsaw, Poland, June 22–26, 2015, 2015

[18] Howard N. Paradoxes of Rationality: Theory of Metagames and Political Behavior, 1971, Cambridge, USA: MA: MIT Press

[19] Kilgour D, Hipel KW, Fang L. The graph model for conflicts. Automatica, 1987, 23(1): 41-55.

[20] Kilgour DM, Hipel KW. The graph model for conflict resolution: Past, present, and future. Group Decision & Negotiation, 2005, 14(6): 441-460.

[21] Kinsara RA, Hipel KW, Kilgour DM. Inverse approach in third party intervention. 2013 IEEE International Conference on Systems, Man, and Cybernetics, Manchester, UK, October 13–16, 2013, 2013

[22] Lee DW, Lai PB. The practice of mediation to resolve clinical, bioethical, and medical malpractice disputes. Hong Kong Medical Journal, 2015, 21(6): 560-564.

[23] Liebman BL. Malpractice mobs: Medical dispute resolution in China. Columbia Law Review, 2013, 113(1): 181-264.

[24] Moore CW. The Mediation Process: Practical Strategies for Resolving Conflict(4ed), 2014, San Francisco, USA: Jossey-Bass

[25] Nash JF. Equilibrium points in n-person games. Proceedings of the National Academy of Sciences of the United States of America, 1950, 36(1): 48-49.

[26] Nash J. Non-cooperative games. Annals of Mathematics, 1951, 54(2): 286-295.

[27] NHFPC National health and family planning commission 2016 annual report on the work of the construction of legal government, 2017

[28] Peng X, Hipel KW, Kilgour DM, Fang L. Representing ordinal preferences in the decision support system gmcr II. IEEE International Conference on Systems, Man, and Cybernetics. Computational Cybernetics and Simulation, Orlando, USA, October 12–15, 1997, 1997

[29] Prein H. Strategies for third party intervention. Human Relations, 1987, 40(11): 699-719.

[30] Regan PM. Conditions of successful third-party intervention in intrastate conflicts. The Journal of Conflict Resolution, 1996, 40(2): 336-359.

[31] Rubin JZ. Experimental research on third-party intervention in conflict: Toward some generalizations. Psychological Bulletin, 1980, 87(2): 379-91.

[32] Sakakibara H, Okada N, Nakase D. The application of robustness analysis to the conflict with incomplete information. IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews), 2002, 32(1): 14-23.

[33] Sakamoto M, Hagihara Y, Hipel KW. Coordination process by a third party in the conflict between Bangladesh and India over regulation of the Ganges River. IEEE International Conference on Systems, Man and Cybernetics, Waikoloa, USA, October 10–10, 2005, 2005

[34] Tsai JF, Lin MH, Hu YC. Finding multiple solutions to general integer linear programs. European Journal of Operational Research, 2008, 184(2): 802-809.

[35] Wang J, Hipel KW, Fang L, Dang Y. Matrix representations of the inverse problem in the graph model for conflict resolution. European Journal of Operational Research, 2018, 270(1): 282-293.

[36] Xu H, Hipel KW, Kilgour DM. Matrix representation of conflicts with two decision-makers. IEEE International Conference on Systems, Man and Cybernetics, Montreal. Canada, October 7–10, 2007, 2007

[37] Xu H, Hipel KW, Kilgour DM. Matrix representation of solution concepts in multiple-decision-maker graph models. IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans, 2008, 39(1): 96-108.

[38] Xu H, Hipel KW, Kilgour DM, Fang L. Conflict Resolution Using the Graph Model: Strategic Interactions in Competition and Cooperation, 2018.

[39] Young OR. The Intermediaries: Third Parties in International Crises, 2015, Princeton, USA: Princeton University Press

[40] Yu J, Hipel KW, Kilgour DM, Zhao M. Option prioritization for unknown preference. Journal of Systems Science and Systems Engineering, 2016, 25(1): 39-61.

[41] Zanjanian H, Abdolabadi H, Niksokhan MH, Sarang A. Influential third party on water right conflict: A game theory approach to achieve the desired equilibrium (case study: Ilam dam, Iran). Journal of Environmental Management, 2018, 214: 283-294.

[42] Zhao M. Evaluation of the third-party mediation mechanism for medical disputes in China. Medicine and Law, 2011, 30(3): 401-415.

[43] Zhong Y. People’s Mediation Skills in Doctor-patient Disputes and Typical Case Analysis, 2015