Large language models (LLMs) have recently shown promise for historical entity linking, but preference optimization for this task is often formulated with only one negative candidate per training instance. This discards information from the remaining candidates retrieved for the same mention. We introduce multi-negative direct preference optimisation (MDPO), a reference-based pairwise objective that compares the correct entity with all valid rejected candidates associated with each mention. MDPO preserves the Bradley-Terry formulation of DPO while exploiting the complete candidate set through masked, length-normalised sequence scores. We evaluate MDPO on hipe-2020 and newseye, covering French, German, English, Swedish, and Finnish historical newspaper text. Experiments show that MDPO improves over supervised fine-tuning and single-negative DPO, with particularly strong gains for NIL mentions, semantic ambiguity, OCR noise, and historically difficult names. Further analyses disentangle candidate-generation and selection errors, showing that candidate retrieval remains a key bottleneck for end-to-end entity linking. These results demonstrate that incorporating all within-instance negative candidates is a simple and effective improvement for LLM-based historical entity linking.

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