Argumentative essays serve as a vital medium for assessing critical thinking and reasoning skills, yet there is limited works on accurately understanding and evaluating such texts via prompt. In this work, we propose TIDE, a novel framework designed to improve criteria-based prompt optimization for argument-related tasks by integrating TrIal and DEbate mechanism. Our method addresses key limitations of criteria-based prompt optimizing by mitigating the influence of noisy training data and enhancing optimization stability. We evaluate TIDE on three core tasks: Automated Essay Scoring, Argument Component Detection, and Argument Relation Identification. Results demonstrate that our framework improves performance across tasks. These findings underscore the potential of combining prompt-based methods for advanced argument understanding.