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The performance of processors in a distributed system can be measured by parameters such as bandwidth, storage capacity, work capability, reliability, manufacture technology, years of usage, among others. An algorithm using a preference-based approach uses these parameters to make decisions. In this paper we introduce a randomized self-stabilizing leader election algorithm for preference-based anonymous trees. Our algorithm uses the preference of the processors as criteria to select a leader under symmetric or non-symmetric configurations. It is partially inspired on Xu and Srimani's algorithm, but we use a distributed daemon and randomization to break symmetry. We prove that our algorithm has an optimal average complexity time and performed simulations to verify our results.