It is conventional wisdom in machine learning and data mining that logical models such as rule sets are more interpretable than other models, and that among such rule-based models, simpler models are more interpretable than more complex ones. In this position paper, we question this latter assumption, and recapitulate evidence for and against this postulate. We also report the results of an evaluation in a crowd-sourcing study, which does not reveal a strong preference for simple rules, whereas we can observe a weak preference for longer rules in some domains. We then continue to review criteria for interpretability from the psychological literature, evaluate some of them, and briefly discuss their potential use in machine learning. On Cognitive Preferences and the Interpretability of Rule-based Models

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