An important problem in descriptive and prescriptive research in decision making is to identify "regions of rationality," i.e., the areas for which simple, heuristic 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 by outlining how our work can be extended to exploring the effects of different loss functions as well as suggesting further topics for future research.
