Abstract:

A committee is a collection of members, where every member has a linear ordering on the alternatives of a finite ground set X. The committee chooses between pairs of alternatives drawn from X by a simple majority vote. The committee's choices induce a preference relation on X. In this paper, we study the possibility of learning preference relations of small committees from examples. We prove that it is impossible to precisely learn the preference relation of a committee before seeing all its choices, even if a teacher guides the learner through the learning process. We also prove that a learner can approximately learn the preference relation of a committee from a relatively few random examples.

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