Large Language Models (LLMs) have shown great potential in code-related software engineering tasks, including code generation, classification, and understanding. While current research primarily focuses on direct inference with single LLMs, this approach may fall short for complex tasks due to ambiguous instructions. To address this limitation, we propose LLM self-negotiation, where multiple LLMs collaborate and debate to reach consensus on code-related tasks. This approach aims to better handle unclear instructions and improve overall effectiveness. We evaluated LLM self-negotiation in three key software engineering domains: Equivalent Mutant Detection (EMD), Automated Vulnerability Detection (AVD), and Automated Program Repair (APR). These domains represent distinct aspects of code-related tasks: functionality understanding, code classification, and code generation, respectively. Our experimental results revealed varying effectiveness across domains. In EMD, LLM self-negotiation demonstrated remarkable improvements, with most models showing performance gains between 114.72% and 351.01% (though CodeLlama experienced a minor 4.5% decrease in F1-score). For APR tasks, self-negotiation performed comparably to single LLM implementations. However, in AVD, the results were mixed - while Vicuna showed improved F1-scores, most models exhibited lower recall rates. These findings indicate that LLM self-negotiation is particularly promising for functionality understanding tasks, while its application to code classification and generation requires further research and refinement.