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Manipulation of positional social choice correspondences under incomplete information

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  • Raffaele Berzi
  • Daniela Bubboloni
  • Michele Gori

Abstract

We study the manipulability of social choice correspondences in situations where individuals have incomplete information about others' preferences. We propose a general concept of manipulability that depends on the extension rule used to derive preferences over sets of alternatives from preferences over alternatives, as well as on individuals' level of information. We then focus on the manipulability of social choice correspondences when the Kelly extension rule is used, and individuals are assumed to have the capability to anticipate the outcome of the collective decision. Under these assumptions, we introduce some monotonicity properties of social choice correspondences whose combined satisfaction is sufficient for manipulability, prove a result of manipulability for unanimous positional social choice correspondences, and present a detailed analysis of the manipulability properties for the Borda, the Plurality and the Negative Plurality social choice correspondences.

Suggested Citation

  • Raffaele Berzi & Daniela Bubboloni & Michele Gori, 2025. "Manipulation of positional social choice correspondences under incomplete information," Papers 2503.23141, arXiv.org.
    • Handle: RePEc:arx:papers:2503.23141
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    References listed on IDEAS

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    1. Gori, Michele, 2021. "Manipulation of social choice functions under incomplete information," Games and Economic Behavior, Elsevier, vol. 129(C), pages 350-369.
    2. Shin Sato, 2008. "On strategy-proof social choice correspondences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(2), pages 331-343, August.
    3. Lin Zhou & Stephen Ching, 2002. "Multi-valued strategy-proof social choice rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(3), pages 569-580.
    4. Kelly, Jerry S, 1977. "Strategy-Proofness and Social Choice Functions without Singlevaluedness," Econometrica, Econometric Society, vol. 45(2), pages 439-446, March.
    5. Zoi Terzopoulou & Ulle Endriss, 2019. "Strategyproof judgment aggregation under partial information," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 53(3), pages 415-442, October.
    6. Barbera, Salvador & Dutta, Bhaskar & Sen, Arunava, 2005. "Corrigendum to "Strategy-proof social choice correspondences" [J. Econ. Theory 101 (2001) 374-394]," Journal of Economic Theory, Elsevier, vol. 120(2), pages 275-275, February.
    7. Barberà, Salvador, 2011. "Chapter Twenty-Five - Strategyproof Social Choice," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 2, chapter 25, pages 731-831, Elsevier.
    8. Zoi Terzopoulou & Ulle Endriss, 2019. "Strategyproof judgment aggregation under partial information," Post-Print hal-04809526, HAL.
    9. Barbera, Salvador, 1977. "Manipulation of social decision functions," Journal of Economic Theory, Elsevier, vol. 15(2), pages 266-278, August.
    10. Prasanta K. Pattanaik, 1975. "Strategic Voting Without Collusion Under Binary and Democratic Group Decision Rules," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 42(1), pages 93-103.
    11. Satterthwaite, Mark Allen, 1975. "Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions," Journal of Economic Theory, Elsevier, vol. 10(2), pages 187-217, April.
    12. Gardenfors, Peter, 1976. "Manipulation of social choice functions," Journal of Economic Theory, Elsevier, vol. 13(2), pages 217-228, October.
    13. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    14. Donald E. Campbell & Jerry S. Kelly & Shaofang Qi, 2018. "A stability property in social choice theory," International Journal of Economic Theory, The International Society for Economic Theory, vol. 14(1), pages 85-95, March.
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