# A characterization of random min–max domains and its applications

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## Abstract

We show that a random rule on a top-connected single-peaked domain is unanimous and strategy-proof if and only if it is a random min–max rule. As a by-product of this result, it follows that a top-connected single-peaked domain is tops-only for random rules. We further provide a characterization of the random min–max domains.

## Keywords

Random min–max rules Single-peaked domains Top-connectedness Uncompromisingness## JEL Classification

D71## Notes

### Acknowledgements

We are grateful to two anonymous referees and the editor for helpful comments. We also thank Gopakumar Achuthankutty, Madhuparna Karmokar, Hans Peters, Arunava Sen, Ton Storcken for useful suggestions and discussion. The usual disclaimer holds.

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