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Cognitive Radios (CRs) are able to operate in a large attribute space and operational parameters are chosen from this space, depending on the sensed environment, to achieve best performance. In this paper we demonstrate that such choice of parameters and the attribute space impact robustness of the network under electronic and information attacks. Such impact results in various tradeoffs to be considered when designing a policy-based CR system. More specifically, we discuss two of the design issues: attribute space size and network cluster size based on these tradeoff considerations. Discussions in the paper show that security and robustness should become an integral part of CR design considerations.