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Michigan-style learning classifier systems (LCSs) are online machine learning techniques that incrementally evolve distributed subsolutions which individually solve a portion of the problem space. As in many machine learning systems, extracting accurate models from problems with class imbalances-that is, problems in which one of the classes is poorly represented with respect to the other classes-has been identified as a key challenge to LCSs. Empirical studies have shown that Michigan-style LCSs fail to provide accurate subsolutions that represent the minority class in domains with moderate and large disproportion of examples per class; however, the causes of this failure have not been analyzed in detail. Therefore, the aim of this paper is to carefully examine the effect of class imbalances on different LCS components. The analysis focuses on XCS, which is the most-relevant Michigan-style LCS, although the models could be easily adapted to other LCSs. Design decomposition is used to identify five elements that are crucial to guaranteeing the success of LCSs in domains with class imbalances, and facetwise models that explain these different elements for XCS are developed. All theoretical models are validated with artificial problems. The integration of all these models enables us to identify the sweet spot where XCS is able to scalably and efficiently evolve accurate models of rare classes; furthermore, facetwise analysis is used as a tool for designing a set of configuration guidelines that have to be followed to ensure convergence. When properly configured, XCS is shown to be able to solve highly unbalanced problems that previously eluded solution.