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

The resolution of real-world conflicts is often supported by third-party intervention (i.e., media? tion). 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.