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This paper examines how disputants’ preferences evolve within conflict management trajectories, addressing a key limitation in Andrew P. Owsiak’s framework, which prioritizes third-party strategies over disputants' agency. By developing a theory of preference convergence, this study identifies three mechanisms—cost recalibration, learning from impasse, and perceived legitimacy—that explain how disputants shift from low-cost diplomatic methods to high-cost legal resolutions over time. Using the Taba arbitration (1982–1988) between Egypt and Israel as a primary case, the article demonstrates that preference shifts are shaped by internal reassessments of political, financial, and reputational costs rather than external pressures alone. The analysis is further enriched by insights from Wiegand and Powell’s strategic forum selection theory and recent judicialization studies from Conflict Management and Peace Science. This integrative approach offers a dynamic understanding of intra-dispute decision-making and highlights broader implications for conflict resolution in protracted territorial disputes.