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Local vote decision fusion is a recently proposed method of target detection for a wireless sensor network in which individual sensors combine their decisions with those of their neighbors and report to a fusion center only if there is a majority in favor of presence. The fusion center reaches a final decision about presence or absence according to whether the number of positive reports exceeds a threshold. This has been shown to give a higher target detection rate, for a specified false alarm rate, than a system in which sensors report their initial decisions directly to the fusion center. A critical aspect of the process is the appropriate setting of the threshold to achieve the specified false alarm rate. We suggest here a simple alternative to the normal approximation proposed previously and demonstrate that this gives more accurate results.