Recent studies show that large language models (LLMs) exhibit self-preference bias when serving as judges, meaning they tend to favor their own responses over those generated by other models. Existing methods typically measure this bias by calculating the difference between the scores a judge model assigns to its own responses and those it assigns to responses from other models. However, this approach conflates self-preference bias with response quality, as higher-quality responses from the judge model may also lead to positive score differences, even in the absence of bias. To address this issue, we introduce gold judgments as proxies for the actual quality of responses and propose the DBG score, which measures self-preference bias as the difference between the scores assigned by the judge model to its own responses and the corresponding gold judgments. Since gold judgments reflect true response quality, the DBG score mitigates the confounding effect of response quality on bias measurement. Using the DBG score, we conduct comprehensive experiments to assess self-preference bias across LLMs of varying versions, sizes, and reasoning abilities. Additionally, we investigate two factors that influence and help alleviate self-preference bias: response text style and the post-training data of judge models. Finally, we explore potential underlying mechanisms of self-preference bias from an attention-based perspective. Our code and data are available at https://github.com/zhiyuanc2001/self-preference.

To alleviate the data scarcity problem in training question answering systems, recent works propose additional intermediate pre-training for dense passage retrieval (DPR). However, there still remains a large discrepancy between the provided upstream signals and the downstream question-passage relevance, which leads to less improvement. To bridge this gap, we propose the HyperLink-induced Pre-training (HLP), a method to pre-train the dense retriever with the text relevance induced by hyperlink-based topology within Web documents. We demonstrate that the hyperlink-based structures of dual-link and co-mention can provide effective relevance signals for large-scale pre-training that better facilitate downstream passage retrieval. We investigate the effectiveness of our approach across a wide range of open-domain QA datasets under zero-shot, few-shot, multi-hop, and out-of-domain scenarios. The experiments show our HLP outperforms the BM25 by up to 7 points as well as other pre-training methods by more than 10 points in terms of top-20 retrieval accuracy under the zero-shot scenario. Furthermore, HLP significantly outperforms other pre-training methods under the other scenarios.