Majority judgment and strategy-proofness: a characterization

Majority judgment as recently formulated and advocated by Balinski and Laraki in their influential monograph (Majority Judgment (2010)) is a method to aggregate profiles of judgments which are expressed in a common language consisting of a linearly ordered, and typically bounded, set of grades. It is shown that majority judgment thus defined is strategy-proof but not coalitionally strategy-proof on a very comprehensive class of rich single peaked preference domains. The proof relies on the key observation that a common bounded linear order of grades makes the set of gradings a product of bounded chains, which is a special instance of a bounded distributive lattice. Relying on the foregoing result, this paper also provides a simple characterization of majority judgment with an odd number of agents by anonymity, bi-idempotence and strategyproofness on rich single peaked domains.