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Weak Equity

Author

Listed:
  • Steven Kivinen

    (University of Graz, Austria)

Abstract

Equal treatment of equals (ETE) is a foundational notion of fairness. However, there are rules that violate ETE while still exhibiting procedural fairness by granting agents symmetric roles. We define weak equity and k-equity (Bartholdi et al., 2021) in a general environment. We show that 2-equity implies ETE under a mild separability condition. Weak equity defines a rich class of rules that often violate ETE. In the fair division environment of Sprumont (1991), we characterize the uniform rule, and sequential allotment rules with equal guarantees (Barbera et al., 1997). Weak equity can give one agent nearly the entire surplus over identical agents.

Suggested Citation

  • Steven Kivinen, 2024. "Weak Equity," Graz Economics Papers 2024-04, University of Graz, Department of Economics.
    • Handle: RePEc:grz:wpaper:2024-04
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    References listed on IDEAS

    as
    1. Laurent Bartholdi & Wade Hann‐Caruthers & Maya Josyula & Omer Tamuz & Leeat Yariv, 2021. "Equitable Voting Rules," Econometrica, Econometric Society, vol. 89(2), pages 563-589, March.
    2. Barbera, Salvador & Jackson, Matthew O. & Neme, Alejandro, 1997. "Strategy-Proof Allotment Rules," Games and Economic Behavior, Elsevier, vol. 18(1), pages 1-21, January.
    3. Sprumont, Yves, 1991. "The Division Problem with Single-Peaked Preferences: A Characterization of the Uniform Allocation Rule," Econometrica, Econometric Society, vol. 59(2), pages 509-519, March.
    4. Kivinen, Steven & Tumennasan, Norovsambuu, 2021. "Robust group strategy-proofness," Theoretical Economics, Econometric Society, vol. 16(4), November.
    5. Nesterov, Alexander S., 2017. "Fairness and efficiency in strategy-proof object allocation mechanisms," Journal of Economic Theory, Elsevier, vol. 170(C), pages 145-168.
    6. Bogomolnaia, Anna & Moulin, Herve, 2001. "A New Solution to the Random Assignment Problem," Journal of Economic Theory, Elsevier, vol. 100(2), pages 295-328, October.
    7. Thomson, William, 2015. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: An update," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 41-59.
    8. Kivinen, Steven, 2023. "On the manipulability of equitable voting rules," Games and Economic Behavior, Elsevier, vol. 141(C), pages 286-302.
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    Keywords

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    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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