Large language models (LLMs) have achieved impressive performance on knowledge-intensive tasks; however, their predictions can be biased due to spurious correlations acquired during pretraining. Recently, debiasing approaches based on front-door adjustment have made substantial progress. Nevertheless, when chain-of-thought (CoT) is used as the mediator, these methods may still be influenced by latent biases, as the CoT generated by LLMs can also be biased. To address this issue, we propose a new paradigm that constructs mediators from sentences with high information gain. Specifically, we first provide a theoretical analysis of mediator properties and prove that valid mediators are variables that yield information gain for the task. Building on this insight, we introduce the Information-Gain Front-Door adjustment (IGFD) framework, which extracts key sentences as mediators from a document via information-gain computation, thereby mitigating biases introduced when LLMs generate mediators. Experiments on document-level multi-hop question answering show that IGFD consistently improves LLM performance and outperforms recent causal-based debiasing methods across both open- and closed-source models. The code and data are publicly available at: https://github.com/xin-miao-cs/IGFD .