# Majority judgment and strategy-proofness: a characterization

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## 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 strategy-proofness on rich single peaked domains*.

## Keywords

Strategy-proofness Bounded distributive lattice Single peakedness Majority rule Majority judgment## Mathematics Subject Classification

05C05 52021 52037## JEL Classification

D71## Notes

### Acknowledgements

Thanks are due to two anonymous reviewers and an Associate Editor for their careful reading of the paper, and their most focussed, helpful and constructive criticisms.

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