  Multi-agent debate system (MAD) imitating the process of human discussion in
pursuit of truth, aims to align the correct cognition of different agents for
the optimal solution. It is challenging to make various agents perform right
and highly consistent cognition due to their limited and different knowledge
backgrounds (i.e., cognitive islands), which hinders the search for the optimal
solution. To address the challenge, we propose a novel
\underline{M}ulti-\underline{A}gent \underline{D}ebate with
\underline{K}nowledge-\underline{E}nhanced framework (\textbf{MADKE}) to
promote the system to find the solution. First, we involve a shared retrieval
knowledge pool in the debate process to solve the problem of limited and
different knowledge backgrounds. Then, we propose an adaptive knowledge
selection method to guarantee the accuracy and personalization of knowledge.
This method allows agents to choose whether to use external knowledge in each
conversation round according to their own needs. Our experimental results on
six datasets show that our method achieves state-of-the-art results compared to
existing single-agent and multi-agent methods. Further analysis reveals that
the introduction of retrieval knowledge can help the agent to break cognitive
islands in the debate process and effectively improve the consistency and
correctness of the model. Moreover, MADKE using Qwen1.5-72B-Chat surpasses
GPT-4 by +1.26\% on average in six datasets, which validates that our method
can help open-source LLMs achieve or even surpass the performance of GPT-4. Our
code is available at \url{https://github.com/FutureForMe/MADKE}.
