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Selection closedness and scoring correspondences

Author

Listed:
  • Semih Koray

    (Bilkent University)

  • Talat Senocak

    (Bilkent University)

Abstract

Universal self-selectivity of a social choice function (SCF) F defined in Koray (Econometrica 68:981–995, 2000) implies that F is either dictatorial or anti-dictatorial. In an attempt to escape this impossibility, here we weaken self-selectivity of an SCF by introducing the notion of selection-closedness pertaining to families of SCFs. As in the self-selectivity setting, a society, which is to make a choice from a set A of alternatives, is also to choose the choice rule that will be employed in making that choice. Self-selectivity of an SCF F requires that F outrivals all available SCFs by selecting itself from among them if it is also used in choosing the choice rule, where the societal preferences on the available SCFs are induced from those on the set A of alternatives in a consequentialist way. Given a collection $${\mathscr {F}}$$ F of SCFs and a nonempty finite set $${\mathcal {A}}$$ A of available SCFs containing also members of $${\mathscr {F}},$$ F , an SCF in $${\mathscr {F}} \cap {\mathcal {A}}$$ F ∩ A is now not required any more to select itself from $${\mathcal {A}},$$ A , but it suffices that it selects some member of $${\mathscr {F}}$$ F for $${\mathscr {F}}$$ F to be selection-closed. It is shown that a proper subset of the collection of all neutral SCFs is selection-closed if and only if all its members are either dictatorships or anti-dictatorships. We further weaken the notion of selection-closedness to an extent that not only enables us to escape the impossibility result, but also equips us with a yardstick to compare correspondences as to whether or not their singleton valued refinements form a weakly selection-closed family. A rich family of scoring correspondences with strict scoring vectors are shown to pass the test of weak selection-closedness, while the Pareto and Condorcet correspondences fail.

Suggested Citation

  • Semih Koray & Talat Senocak, 2024. "Selection closedness and scoring correspondences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 63(1), pages 179-202, August.
  • Handle: RePEc:spr:sochwe:v:63:y:2024:i:1:d:10.1007_s00355-024-01529-y
    DOI: 10.1007/s00355-024-01529-y
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    References listed on IDEAS

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    1. Salvador Barbera & Matthew O. Jackson, 2004. "Choosing How to Choose: Self-Stable Majority Rules and Constitutions," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 119(3), pages 1011-1048.
    2. Daron Acemoglu & Georgy Egorov & Konstantin Sonin, 2012. "Dynamics and Stability of Constitutions, Coalitions, and Clubs," American Economic Review, American Economic Association, vol. 102(4), pages 1446-1476, June.
    3. Semih Koray, 2000. "Self-Selective Social Choice Functions Verify Arrow and Gibbarad- Satterthwaite Theorems," Econometrica, Econometric Society, vol. 68(4), pages 981-996, July.
    4. Semih Koray & Bulent Unel, 2003. "Characterization of self-selective social choice functions on the tops-only domain," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 20(3), pages 495-507, June.
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