of research on interpretability. More interpretable models are being pursued not only for more complex techniques such as deep neural networks but also for more traditional models, like the interpretable *decision lists* proposed by Letham et al. [-@letham2013interpretable]. A decision list is a series of *if-then-else* statements, where the *if* statements define a partition of a set of features, the *then* statements define a predicted outcome, and the *else* statements define either a new rule to be applied (if followed by another *if* statement) or a default outcome to be assumed as the prediction, in case none of the previous rules were assessed as true. The proposed approach, called Bayesian List Machine (BLM), “produces a posterior distribution over permutations of *if...then...* rules, starting from a large set of possible pre-mined rules” [@letham2013interpretable]. The authors follow the assumption that the model is intrinsically interpretable because, given their format, the rules naturally provide a reason for the prediction they lead to. However, no quantitative or qualitative evaluation is presented regarding the model’s interpretability assessment.

![image](sets_vs_lists){width="\textwidth"}

Lakkaraju et al. [-@lakkaraju2016interpretable] introduced a predictive model based on interpretable *decision sets* (DSs): sets of independent *if-then* rules aimed at being human-interpretable while still showing high 