<p>In conflict mediation, guiding stakeholders to make concessions among the three preference relations (more preferred, less preferred, and equally preferred) presents varying degrees of difficulty. This study proposes a novel algebraic expression where a specific numerical value can represent all scenarios of transitions among preference relations to accurately quantify the differences in preference concessions made by decision-makers. Furthermore, considering the degrees of difficulty in preference relation transitions, an enhanced third-party conflict mediation model is purposefully constructed to determine the minimal preference concessions needed to achieve the target state of mediation. Finally, we implement the proposed third-party conflict resolution approach in mediating the doctor–patient dispute to demonstrate its practical application.</p>