Fair division of indivisible items between two people with identical preferences: Envy-freeness, Pareto-optimality, and equity

This paper focuses on the fair division of a set of indivisible items betwe en two people when both have the same linear preference order on the items but may have different preferences over subsets of items. Surprisingly, div isions that are envy-free, Pareto-optimal, and ensure that the less well-of f person does as well as possible (i.e., are equitable) can often be achiev ed. Preferences between subsets are assumed to satisfy axioms of qualitativ e probability without implying the existence of additive utilities, which i s treated as a special case. Algorithms that render fair division practicab le are proposed, and their vulnerability to strategic manipulation is inves tigated.