Large Language Models (LLMs) have demonstrated superior listwise ranking performance. However, their superior performance often relies on large-scale parameters (\eg, GPT-4) and a repetitive sliding window process, which introduces significant efficiency challenges. In this paper, we propose \textbf{CoRanking}, a novel collaborative ranking framework that combines small and large ranking models for efficient and effective ranking. CoRanking first employs a small-size reranker to pre-rank all the candidate passages, bringing relevant ones to the top part of the list (\eg, top-20). Then, the LLM listwise reranker is applied to only rerank these top-ranked passages instead of the whole list, substantially enhancing overall ranking efficiency. Although more efficient, previous studies have revealed that the LLM listwise reranker have significant positional biases on the order of input passages. Directly feed the top-ranked passages from small reranker may result in the sub-optimal performance of LLM listwise reranker. To alleviate this problem, we introduce a passage order adjuster trained via reinforcement learning, which reorders the top passages from the small reranker to align with the LLM's preferences of passage order. Extensive experiments on three IR benchmarks demonstrate that CoRanking significantly improves efficiency (reducing ranking latency by about 70\%) while achieving even better effectiveness compared to using only the LLM listwise reranker.

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