We consider a binary parallel decentralized detection system. It employs n local detectors (LDs) to observe a binary phenomenon in order to accept one of two hypotheses about the phenomenon (hypothesis H0 or hypothesis H1). Each LD uses a local decision rule to compress its local observations into a binary local decision. The Data Fusion Center (DFC) uses a fusion rule to combine all binary local decisions into a global binary decision. The combination of the global fusion rule and all local decision rules in the system is referred to as a decision strategy. In many scenarios, the system uses a single (deterministic) decision strategy - the DFC used a single deterministic fusion rule and each LD uses a single deterministic decision rule. A randomized strategy involves a randomized or pseudo - randomized choice between several deterministic decision strategies. In some instances, such randomized strategy is needed to ensure that the Receiver Operator Characteristic (ROC) curve of the architecture is convex. We are interested in scenarios that require that the randomized strategy be coordinated between the DFC and the LDs, maintaining synchronization between the selection scheme of local decision rules and global fusion rules. Circumstances that require such coordinated randomized selection are labeled 'dependent randomization.' We present systems that use dependent randomization, and also discuss their response when synchronization is occasionally lost.