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Distributed decision making is an intrinsic ingredient of ad-hoc and self-organized wireless networks. For a special type of distributed algorithms, called consensus algorithms, the convergence properties are explored here for a keyhole geometry when the nodes communicate over a wireless channel. The behaviour of the algorithm is analysed from both a graph theoretic perspective and its application to time-offset estimation for different time-varying conditions of the wireless channel depending on the channel coherence time. Two convergence regimes are identified which depend on the keyhole size. The bottleneck effect induced by the keyhole geometry is significant and hence requires geometry aware modifications to conventional consensus algorithms. These findings could suggest new directions for improved versions of the consensus algorithms for wireless networks.