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In a distributed information retrieval system, how to merge results from different text databases is an important issue, since it affects the effectiveness of the result considerably. In many cases, the underlining systems only provide a ranked list of documents for any information need. In this paper, we investigate the relation between rank and relevance in resultant document lists, and find that the cubic model is a good option for this. Extensive experimentation is conducted to evaluate the performance of the cubic model for results merging. The experimental results demonstrate that the cubic model is better than the logistic model, which was suggested by a previous research.