Prompt Lottery in LLM-as-a-Judge: Measuring and Mitigating Sensitivity to Syntactic Rephrasing

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LLM-as-a-Judge has become a standard for evaluating large language models, yet most approaches implicitly assume that a single judge prompt functions as a stable evaluation instrument. Prior work has primarily explored deliberate prompt modifications such as scoring rubrics, role descriptions, or chain-of-thought reasoning in order to optimize accuracy. In contrast, we investigate whether validated prompt variants intended to preserve evaluation semantics while differing in surface realization (\textit{paraphrastic rephrasings}) yield consistent judgments under a fixed evaluation task. We introduce \textit{Prompt Lottery}, a phenomenon in which paraphrastic rephrasings produce different LLMaJ judgments. Across a large-scale study spanning diverse evaluation tasks, judge families, and model backbones, we find that these variations can alter evaluation outcomes and, in some settings, reverse relative model rankings. A user study with 10 human annotators shows that LLMaJ judges exhibit 6-9$\times$ larger agreement degradation under prompt rephrasings than humans, falling below the generally accepted threshold in usability studies. This indicates that single-prompt evaluation is insufficiently robust for model ranking. Finally, we show that multi-prompt aggregation substantially improves robustness by emphasizing judgments that remain consistent across prompt variants.