Fact-checking explanations help Web users understand why a claim receives its verdict, yet the same explanation may not satisfy readers with different backgrounds and preferences. We formulate Faithful Personalized Fact-Checking Explanation Rewriting, which adapts an existing explanation to individual readers while preserving factual fidelity. Rather than relying on reader-written reference explanations, we learn personalized rewriting from the relative preferences of LLM-simulated readers. However, this presents two challenges: distinguishing persona-specific preferences from general explanation quality and learning beyond a limited set of predefined explanation styles. To address these challenges, we propose Personalized Explanation Rewriting via Preference Learning (PERPL), a framework consisting of two components. Simulated Preference Construction derives persona-specific supervision from simulated reader preferences through cross-persona reciprocal pairing. Progressive Preference Learning first trains a lightweight rewriter on the constructed supervision and then refines it through exploration-guided preference optimization, enabling it to discover preferred explanations beyond the predefined styles. Extensive experiments demonstrate that PERPL outperforms much larger general-purpose LLMs in personalized preference alignment while maintaining high factual fidelity.

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