Efficient allocation with ordinal preference intensities

Abstract

Standard allocation methods that rely on ordinal preferences ignore how strongly agents value different improvements. On the other hand, methods based on cardinal utilities require assumptions that are often considered too demanding. This paper studies the classic one-to-one assignment problem in the middle-ground environment of *ordinal* preference intensities: agents rank alternatives as well as preference improvements, without necessarily being able to quantify these comparisons. The paper introduces an interpersonal comparability assumption for this novel social-choice analytical setting. Building on it, it proposes and analyses the *intensity-efficiency* criterion. This refines Pareto's criterion by discarding any allocation that is worse than another according to an intuitive intensity-dominance relation. The feasibility and applicability of this framework in matching problems is illustrated with two quadratic-time algorithms which, respectively, elicit ordinal intensity rankings and extend the classic Random Priority mechanism in a welfare-improving direction.