An important problem faced by boundedly rational agents is to identify "regions of rationality," i.e., the areas for which simple, boundedly rational models are and are not effective. To map the contours of such regions, we derive probabilities that models identify the best of m alternatives (m > 2) characterized by k attributes (k > 1). The models include a single variable (lexicographic), variations of elimination-by-aspects, equal weighting, hybrids of the preceding, and models exploiting dominance. We compare all with multiple regression. We illustrate the theory with twenty simulated and four empirical datasets. Fits between predictions and realizations are excellent. However, the terrain mapped by our work is complex and no single model is "best." We further provide an overview by regressing the performance of the different models on factors characterizing environments. We conclude with suggestions for further research as well as implications for the concept of rationality in economics.