This study examines the problem of target detection by a wireless sensor network. Sensors acquire measurements emitted from the target that are corrupted by noise and initially make individual decisions about the presence/absence of the target. We propose the Local Vote Decision Fusion algorithm, in which sensors first correct their decisions using decisions of neighboring sensors, and then make a collective decision as a network. An explicit formula that approximates the system's decision threshold for a given false alarm rate is derived using limit theorems for random fields, which provides a theoretical performance guarantee for the algorithm. We examine both distance- and nearest neighbor-based versions of the local vote algorithm for grid and random sensor deployments and show that, for a fixed system false alarm, the local vote correction achieves significantly higher target detection rate than decision fusion based on uncorrected decisions. The local vote decision fusion f...