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Local global equivalence in voting models: a characterization and applications

Author

Listed:
  • Kumar, Ujjwal

    (Economic Research Unit, Indian Statistical Institute, Kolkata)

  • Roy, Souvik

    (Economic Research Unit, Indian Statistical Institute, Kolkata)

  • Sen, Arunava

    (Economics and Planning Unit, Indian Statistical Institute, New Delhi, India)

  • Yadav, Sonal

    (Department of Economics, Umea University)

  • Zeng, Huaxia

    (School of Economics, Shanghai University of Finance and Economics)

Abstract

The paper considers a voting model where each voter's type is her preference. The type graph for a voter is a graph whose nodes are the possible types of the voter. A social choice function is locally strategy-proof if no type of a voter can gain by misrepresentation to a type that is connected to her true type by an edge in the type graph. A social choice function is strategy-proof if no type of a voter can gain by misrepresentation to an arbitrary type. Local-Global equivalence (LGE) is satisfied if local strategy-proofness implies strategy-proofness. The paper identifies a condition on the graph that characterizes LGE. Our notion of ``localness'' is perfectly general - we use this feature of our model to identify notions of localness according to which various models of multi-dimensional voting satisfy LGE. Finally, we show that LGE for deterministic social choice functions does not imply LGE for random social choice functions.

Suggested Citation

  • 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.
    • Handle: RePEc:the:publsh:4177
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    Citations

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    Cited by:

    1. Roy, Souvik & Sadhukhan, Soumyarup, 2022. "On the equivalence of strategy-proofness and upper contour strategy-proofness for randomized social choice functions," Journal of Mathematical Economics, Elsevier, vol. 99(C).
    2. Shurojit Chatterji & Huaxia Zeng, 2023. "Decomposability and Strategy-proofness in Multidimensional Models," Papers 2303.10889, arXiv.org, revised Nov 2023.
    3. 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).
    4. Kumar, Ujjwal & Roy, Souvik, 2021. "Local incentive compatibility in ordinal type-spaces," MPRA Paper 110994, University Library of Munich, Germany.
    5. Altuntaş, Açelya & Phan, William & Tamura, Yuki, 2023. "Some characterizations of Generalized Top Trading Cycles," Games and Economic Behavior, Elsevier, vol. 141(C), pages 156-181.
    6. Stergios Athanasoglou & Somouaoga Bonkoungou & Lars Ehlers, 2023. "Strategy-proof preference aggregation and the anonymity-neutrality tradeoff," Working Papers 519, University of Milano-Bicocca, Department of Economics.
    7. Miho Hong & Semin Kim, 2023. "Unanimity and local incentive compatibility in sparsely connected domains," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 61(2), pages 385-411, August.

    More about this item

    Keywords

    Local incentive constraints; strategy-proofness; mechanism design; strategic voting;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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