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Decomposability and Strategy-proofness in Multidimensional Models

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  • Shurojit Chatterji
  • Huaxia Zeng

Abstract

We introduce the notion of a multidimensional hybrid preference domain on a (finite) set of alternatives that is a Cartesian product of finitely many components. We demonstrate that in a model of public goods provision, multidimensional hybrid preferences arise naturally through assembling marginal preferences under the condition of semi-separability - a weakening of separability. The main result shows that under a suitable "richness" condition, every strategy-proof rule on this domain can be decomposed into component-wise strategy-proof rules, and more importantly every domain of preferences that reconciles decomposability of rules with strategy-proofness must be a multidimensional hybrid domain.

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  • Shurojit Chatterji & Huaxia Zeng, 2023. "Decomposability and Strategy-proofness in Multidimensional Models," Papers 2303.10889, arXiv.org, revised Nov 2023.
    • Handle: RePEc:arx:papers:2303.10889
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    References listed on IDEAS

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    1. Sato, Shin, 2013. "A sufficient condition for the equivalence of strategy-proofness and nonmanipulability by preferences adjacent to the sincere one," Journal of Economic Theory, Elsevier, vol. 148(1), pages 259-278.
    2. Chatterji, Shurojit & Zeng, Huaxia, 2019. "Random mechanism design on multidimensional domains," Journal of Economic Theory, Elsevier, vol. 182(C), pages 25-105.
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    6. Chatterji, Shurojit & Sanver, Remzi & Sen, Arunava, 2013. "On domains that admit well-behaved strategy-proof social choice functions," Journal of Economic Theory, Elsevier, vol. 148(3), pages 1050-1073.
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    8. Chatterji, Shurojit & Roy, Souvik & Sadhukhan, Soumyarup & Sen, Arunava & Zeng, Huaxia, 2022. "Probabilistic fixed ballot rules and hybrid domains," Journal of Mathematical Economics, Elsevier, vol. 100(C).
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    10. Chatterji, Shurojit & Zeng, Huaxia, 2023. "A taxonomy of non-dictatorial unidimensional domains," Games and Economic Behavior, Elsevier, vol. 137(C), pages 228-269.
    11. Kumar, Ujjwal & Roy, Souvik & Sen, Arunava & Yadav, Sonal & Zeng, Huaxia, 2021. "Local global equivalence in voting models: a characterization and applications," Theoretical Economics, Econometric Society, vol. 16(4), November.
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