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.

Vannucci, S. (2019). Majority judgment and strategy-proofness: a characterization. INTERNATIONAL JOURNAL OF GAME THEORY, 48(3), 863-886 [10.1007/s00182-019-00666-4].

Majority judgment and strategy-proofness: a characterization

Stefano Vannucci
2019-01-01

Abstract

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.
Vannucci, S. (2019). Majority judgment and strategy-proofness: a characterization. INTERNATIONAL JOURNAL OF GAME THEORY, 48(3), 863-886 [10.1007/s00182-019-00666-4].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11365/1070886