In the 1960's, the logistic regression model from statistics and the binary probit model from psychology were linked with random utility theory, thereby connecting such methods with economic theory. Since then, the fields of statistics, computer science, and machine learning have created numerous methods for modeling discrete choices. However, these newer methods have not been derived from or linked with economic theories of human decision making. We believe this lack of economic interpretation is one reason discrete choice modelers have been slow to adopt these newer methods.Our paper begins bridging this gap by providing a microeconomic framework for decision trees: a popular machine learning method. Specifically, we show how decision trees represent a non-compensatory decision protocol known as disjunctions-of-conjunctions and how this protocol generalizes many of the noncompensatory rules used in the discrete choice literature so far. Additionally, we show how existing decision tree variants address many economic concerns that choice modelers might have. Beyond theoretical interpretations, we contribute to the existing literature of two-stage, semi-compensatory modeling and to the existing decision tree literature. In particular, we formulate the first bayesian model tree, thereby allowing for uncertainty in the estimated non-compensatory rules as well as for context-dependent preference heterogeneity in one's second-stage choice model. Using an application of bicycle mode choice in the San Francisco Bay Area, we estimate our bayesian model tree, and we find that it is over 1,000 times more likely to be closer to the true data-generating process than a multinomial logit model (MNL). Qualitatively, our bayesian model tree automatically finds the effect of bicycle infrastructure investment to be moderated by travel distance, socio-demographics and topography, and our model identifies diminishing returns from bicycle lane investments. These qualitative differences lead the bayesian model trees to produce forecasts that directly align with the observed bicycle mode shares in regions with abundant bicycle infrastructure such as Davis, CA and the Netherlands. In comparison, the forecasts of the MNL model are overly optimistic.