We introduce partial lexicographic preference trees (PLPtrees) as a formalism for compact representations of preferences over combinatorial domains. Our main results concern the problem of passive learning of PLP-trees. Specifically, forseveral classes of PLP-trees, we study how to learn (i) a PLP-tree consistent with a dataset of examples, possibly subject to requirements on the size of the tree, and (ii) a PLP-tree correctly ordering as many of the examples as possible in case the dataset of examples is inconsistent. We establish complexity of these problems and, in all cases where the problem is in the class P, propose polynomial time algorithms.

Fast and frugal heuristics are well studied models of bounded rationality. Psychological research has proposed the take-the-best heuristic as a successful strategy in decision making with limited resources. Take-thebest searches for a sufficiently good ordering of cues (features) in a task where objects are to be compared lexicographically. We investigate the complexity of the problem of approximating optimal cue permutations for lexicographic strategies. We show that no efficient algorithm can approximate the optimum to within any constant factor, if P NP. We further consider a greedy approach for building lexicographic strategies and derive tight bounds for the performance ratio of a new and simple algorithm. This algorithm is proven to perform better than take-the-best.

Fast and frugal heuristics are well studied models of bounded rationality. Psychological research has proposed the take-the-best heuristic as a successful strategy in decision making with limited resources. Take-thebest searches for a sufficiently good ordering of cues (features) in a task where objects are to be compared lexicographically. We investigate the complexity of the problem of approximating optimal cue permutations for lexicographic strategies. We show that no efficient algorithm can approximate the optimum to within any constant factor, if P NP. We further consider a greedy approach for building lexicographic strategies and derive tight bounds for the performance ratio of a new and simple algorithm. This algorithm is proven to perform better than take-the-best.

Fast and frugal heuristics are well studied models of bounded rationality. Psychologicalresearch has proposed the take-the-best heuristic as a successful strategy in decision making with limited resources. Take-thebest searchesfor a sufficiently good ordering of cues (features) in a task where objects are to be compared lexicographically. We investigate the complexity of the problem of approximating optimal cue permutations for lexicographic strategies. We show that no efficient algorithm can approximate theoptimum to within any constant factor, if P NP. We further consider a greedy approach for building lexicographic strategies and derive tight bounds for the performance ratio of a new and simple algorithm. This algorithm is proven to perform better than take-the-best.