“Recently, there has been a trend of evaluating the Large Language Model (LLM) quality in theflavor of LLM-as-a-Judge, namely leveraging another LLM to evaluate the current output qual-ity. However, existing judges are proven to be biased, namely they would favor answers whichpresent better superficial quality (such as verbosity, fluency) while ignoring the instruction fol-lowing ability. In this work, we propose systematic research about the bias of LLM-as-a-Judge.Specifically, for closed-source judge models, we apply calibration to mitigate the significance ofsuperficial quality, both on probability level and prompt level. For open-source judge models, wepropose to mitigate the bias by contrastive training, with curated negative samples that deviatefrom instruction but present better superficial quality. We apply our methods on the bias evalu-ation benchmark, and experiment results show our methods mitigate the bias by a large marginwhile maintaining a satisfactory evaluation accuracy.”