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In a distributed database system, data replicas are placed at different locations to achieve high data availability in the presence of link failures. With majority voting protocol, a location is survived for read/write operations if and only if it is accessible to more than half of the replicas. The problem is to find out the optimal placements for a given number of data replicas in a ring network. When the number of replicas is odd, it was conjectured by Hu et al. that every uniform placement is optimal, which is proved by Shekhar and Wu later. However, when the number of replicas is even, it was pointed out by Hu et al. that uniform placements are not optimal and the optimal placement problem may be very complicated. In this paper, we study the optimal placement problem in a ring network with majority voting protocol and even number of replicas, and give a complete characterization of optimal placements when the number of replicas is not too large compared with the number of locations.