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Spectrum sensing is a key problem in cognitive radio (CR). Because of a low SNR, fading and sensing time constraints, a single CR may not be able to reliably sense the presence of primary radios, which motivates the study of sensing by multiple cognitive users. Here, the authors consider cooperative spectrum sensing (CSS) using a counting rule where several cognitive users sense whether primary users exist or not and send their decisions to the centre where the final decision is made. Optimal strategies under both the Neyman-Pearson criterion and the Bayesian criterion for CSS are derived using a counting rule. In addition, the authors present simple methods to calculate the optimal settings. Another contribution here is the analysis of a randomised rule at the centre, which is a long-existing problem in the field of distributed detection systems.