Maximal and Supremal Domains for Strategy-Proofness

17 Pages Posted: 28 Nov 2001

See all articles by Stephen Ching

Stephen Ching

School of Economics and Finance, The University of Hong Kong

Shigehiro Serizawa

Tohoku University; University of Shiga

Date Written: November 22, 2001


In this paper, we pose the following question in a private-good model. To what extent can the single-peaked domain be enlarged while preserving the existence of rules satisfying strategy-proofness, symmetry and unanimity? This formulation is adopted for three reasons. First, it marks a clear distinction between the two existing approaches to the maximal domain question in the literature. Second, it restores the role of strategy-proofness, which is suppressed by efficiency in an earlier result (Ching and Serizawa, 1998). Third, a private-good model allows us to conduct a richer analysis of strategy-proof rules. We show that the weakly single-peaked domain is the unique maximal domain for strategy-proofness, symmetry and unanimity. The weakly single-peaked domain is marginally bigger than the single-peaked domain. A diagnosis of the result reveals that maximal domain can be a stringent concept. A less stringent concept is proposed: supermal domain. (Supremal domain is analogous to the concept of supremum in an open interval.) All supermal domains for strategy-proofness, symmetry and unanimity are shown to be strictly smaller than the convex domain, which is slightly bigger than the weakly single-peaked domain. These results indicate that the assumption of single-peakedness essentially cannot be dispensed with if one is interested in strategy-proofness.

Keywords: Strategy-proofness, Single-peakedness, Maximal and Supremal Domains

JEL Classification: C72, D78

Suggested Citation

Ching, Stephen and Serizawa, Shigehiro, Maximal and Supremal Domains for Strategy-Proofness (November 22, 2001). Available at SSRN: or

Stephen Ching

School of Economics and Finance, The University of Hong Kong ( email )

Pokfulam Road
Hong Kong

Shigehiro Serizawa (Contact Author)

Tohoku University ( email )

SKK Building, Katahira 2
Graduate School of Economics
Aoba-ku, Sendai, 980-8577

University of Shiga

Hikone, Shiga, 522-8522

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